ສົມຜົນຈຸນລະຄະນິດ Differential Equations

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(D4 \uf02d1) y \uf03d ex cos 2x \u0ea7\u0eb4\u0e97\u0eb5\u0ec1\u0e81:\u0ec9 \u0e8a\u0ead\u0e81\u0eab\u0eb3 yc \u0e88\u0eb3\u0e81\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99 (D4 \uf02d1) y \uf03d 0 \u0eaa\u0ebb\u0ea1\u0e9c\u0e99\u0ebb \u0e8a\u0ea7\u0ec8 \u0e8d\u0ec1\u0ea1\u0ec8\u0e99 r4 \uf02d1 \uf03d 0 (r \uf02d1)(r \uf02b1)(r2 \uf02b1) \uf03d 0 r \uf03d \uf02d1;1; \uf0b1i \u0eaa\u0eb0\u0e99\u0e99\u0eb1\u0ec9 yc \uf03d c1e\uf02dx \uf02b c2ex \uf02b c3 cos x \uf02b c4 sin x \u0e88\u0eb3\u0e81 (D4 \uf02d1) y \uf03d ex cos 2x 1 D4 \uf02d1 \uf028 \uf029\u0e88\u0eb0\u0ec4\u0e94\u0ec9 yp \uf03d ex cos 2x \u0ead\u0eb4\u0e87\u0e95\u0eb3\u0ea1\u0eaa\u0eb9\u0e94 1 f (x) cos ax \uf03d Re \uf0e6 1 f ( x)eiax \uf0f6 Q(D) \uf0e7 Q(D) \uf0f7 \uf0e8 \uf0f8 \u0eaa\u0eb0\u0e99\u0ec9\u0e99\u0eb1 yp \uf03d Re \uf0e6 1 e x \uf0d7 ei2x \uf0f6 \uf03d Re \uf0e6 1 e\uf0281\uf02bi 2\uf029 x \uf0f6 \u0ec2\u0e94\u0e8d\u0e97\u0eb5\u0ec8 f (x) \uf03d ex; a \uf03d 2 \uf0e8\uf0e7 4\uf02d \uf0f8\uf0f7 \uf0e7\uf0e8 4\uf02d \uf0f8\uf0f7 D 1 D 1 \u0e95\u0eb3\u0ea1\u0eaa\u0eb9\u0e94 1 eax \uf03d 1 eax \u0ec0\u0ea1\u0ec8\u0eb7\u0ead\u0eb5 Q(a) \uf0b9 0 Q(D) Q(a) \u0e88\u0eb0\u0ec4\u0e94\u0ec9 yp \uf03d \uf0e6 \uf0281\uf02b 1 e\uf0281\uf02bi 2\uf029 x \uf0f6 Re \uf0e7\uf0e8\uf0e7 \uf02d1 \uf0f7\uf0f7\uf0f8 2i \uf0294 \uf028 \uf029\uf0e6 \uf028 \uf029 \uf02b \uf0281\uf0292 1 \uf02b \uf0281\uf029 \uf028 \uf0293 \uf02b \uf028 \uf0294 \uf02d1 e\uf0281\uf02b 2i \uf029 x \uf0f6 \uf0f7 \uf03d Re\uf0e7 2i 6 \uf028 2i \uf0292 4 2i 2i \uf0f8\uf0f7 \uf0e7\uf0e8 1\uf02b 4 12 148","\uf03d Re \uf0e6 1 e\uf0281\uf02b 2i \uf029 x \uf0f6 \uf0e8\uf0e7 \uf02d \uf0f8\uf0f7 \uf02d8 24i \uf03d Re \uf0e6 1 \uf0d7 \uf02d8 \uf02b 24i e\uf0281\uf02b2i \uf029x \uf0f6 \uf0e8\uf0e7 \uf02d \uf02d8 \uf02b 24i \uf0f7\uf0f8 \uf02d8 24i \uf03d Re \uf0e6 \uf02d8 \uf02b 24i e\uf0281\uf02b 2i \uf029 x \uf0f6 \uf0e7\uf0e8 64 \uf02b 576 \uf0f7\uf0f8 \uf03d R e \uf0e6 \uf02d8 \uf02b 24i e\uf0281\uf02b 2i \uf029 x \uf0f6 \uf0e7\uf0e8 640 \uf0f8\uf0f7 \uf03d Re \uf0e6 1 e x \uf028 \uf02d8 \uf02b 24i \uf029 e2ix \uf0f6 \uf0e8\uf0e7 640 \uf0f7\uf0f8 \uf03d Re \uf0e6 1 e x \uf028 \uf02d8 \uf02b 24i \uf029 \uf028 cos 2 x \uf02b i sin 2 x \uf029 \uf0f6 \uf0e7\uf0e8 640 \uf0f7\uf0f8 \uf03d Re \uf0e6 1 e x \uf028 \uf02d8 cos 2 x \uf02d 24 sin 2 x \uf02b \uf028 24i cos 2 x \uf02d 8i sin 2 x \uf029 \uf029 \uf0f6 \uf0e8\uf0e7 640 \uf0f7\uf0f8 \uf03d 1 ex \uf028\uf02d8cos 2x \uf02d 24sin 2x\uf029 640 \uf03d \uf02d 1 ex \uf028cos 2x \uf02b 3sin 2x\uf029 80 \u0e94\u0e87\u0ec8\u0eb1 \u0e99\u0eb1\u0e99\u0ec9 ,\u0e9c\u0e99\u0ebb \u0eaa\u0eb0\u0ec0\u0ea5\u0ec8\u0e8d\u0e97\u0ebb\u0ec8\u0eb1\u0ea7\u0ec4\u0e9b\u0ec1\u0ea1\u0ec8\u0e99 y \uf03d yc \uf02b yp y \uf03d c1e\uf02d x \uf02b c2ex \uf02b c3 cos x \uf02b c4 sin x \uf02d 1 ex \uf028cos 2x \uf02b 3sin 2x\uf029 80 5. \u0e88\u0ebb\u0eb1\u0ec8\u0e87\u0eab\u0eb3\u0e9c\u0ebb\u0e99\u0eaa\u0eb0\u0ec0\u0ea5\u0e8d\u0ec8 \u0e97\u0eb1\u0ec8\u0ea7\u0ebb \u0ec4\u0e9b\u0e82\u0ead\u0e87\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99\u0e88\u0eb8\u0e99\u0ea5\u0eb0\u0e84\u0eb0\u0e99\u0eb4\u0e94\u0e95\u0ec8\u0ecd\u0ec4\u0e9b\u0e99\u0ec9\u0eb1\u0eb5 1. y\uf0a2\uf0a2 \uf02b y \uf03d cos ecx \u0ea7\u0e97\u0eb4 \u0ec1\u0eb5 \u0e81:\u0ec9 \u0e8a\u0ead\u0e81\u0eab\u0eb3 yc \u0e88\u0eb3\u0e81\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99 y\uf0a2\uf0a2 \uf02b y \uf03d 0 \u0eaa\u0ea1\u0ebb \u0e9c\u0ebb\u0e99\u0e8a\u0ea7\u0ec8 \u0e8d\u0ec1\u0ea1\u0ec8\u0e99 r2 \uf02b1 \uf03d 0 \uf0de r \uf03d \uf0b1i \u0eaa\u0eb0\u0e99\u0ec9\u0e99\u0eb1 yc \uf03d c1 cos x \uf02b c2 sin x \u0ec2\u0e94\u0e8d\u0e97\u0eb5 y1 \uf03d cos x; y2 \uf03d sin x \u0eaa\u0ebb\u0ea1\u0ea1\u0eb8\u0e94\u0e9c\u0ebb\u0e99\u0eaa\u0eb0\u0ec0\u0ea5\u0e8d\u0ec8 \u0eaa\u0eb0\u0ec0\u0e9e\u0eb3\u0eb0\u0e84\u0ec8\u0eb5\u0eb7 yp \uf03d v1 cos x \uf02b v2 sin x \u0e81\u0eb3\u0e99\u0e94\u0ebb \u0ec0\u0e87\u0eb5\u0ead\u0ec8\u0eb7 \u0e99\u0ec4\u0e82\u0ec0\u0e9e\u0eb5\u0ead\u0eb7\u0ec8 \u0e88\u0eb0\u0eab\u0eb3\u0e84\u0ec8\u0eb3 v1 \u0ec1\u0ea5\u0eb0 v2 \u0e88\u0eb3\u0e81\u0ea5\u0eb0\u0e9a\u0ebb\u0e9a\u0eaa\u0ea1\u0ebb \u0e9c\u0e99\u0ebb \u0e94\u0e87\u0eb1\u0ec8 \u0e99\u0eb1\u0eb5\u0ec9: \uf0ec\uf0efv1\uf0a2y1 \uf02b v2\uf0a2 y2 \uf03d 0 f (x) \uf0ef\uf0ee\uf0edv1\uf0a2y1\uf0a2 \uf02b v2\uf0a2 y2\uf0a2 a0 \uf03d \u0e88\u0eb3\u0e81 (D2 \uf02b1) y \uf03d cos ecx \u0e88\u0eb0\u0ec4\u0e94\u0ec9 f (x) \uf03d cos ecx , a \uf03d 1 \u0e88\u0eb0\u0ec4\u0e94\u0ea5\u0ec9 \u0eb0\u0e9a\u0e9a\u0ebb \u0eaa\u0ebb\u0ea1\u0e81\u0eb3\u0e99\u0ec1\u0ea1\u0e99\u0ec8 \uf0ee\uf0ec\uf0edv\uf02d1\uf0a2vc1\uf0a2ossinxx\uf02b\uf02bv2v\uf0a2 2\uf0a2sicnoxs \uf03d0 cos ecx x\uf03d 149","\u0e8a\u0ead\u0e81\u0e84\u0eb3\u0ec8 v1, v2 \u0ec2\u0e94\u0e8d\u0ec3\u0e8a\u0e81\u0ec9 \u0ebb\u0e94\u0ec0\u0e81\u0e99\u0e81\u0ea3\u0eb3\u0ec0\u0ea1\u0e94\u0eb5 \u0e87\u0ec8\u0eb1 \u0e99:\u0ec9\u0eb1\u0eb5 w \uf03d cos x sin x \uf03d cos2 x \uf02b sin2 x \uf03d 1 \uf02d sin x cos x 0 sin x v1\uf0a2 \uf03d cos ecx cos x \uf03d \uf02d1 1 \uf0de v1 \uf03d \uf0f2 v1\uf0a2dx \uf03d \uf02d\uf0f21dx \uf03d \uf02dx cos x 0 v2\uf0a2 \uf03d \uf02dsin x cos ecx \uf03d \uf028cos x\uf029\uf028cos ecx\uf029 \uf02d \uf028\uf02dsin x\uf029\uf0280\uf029 \uf03d cotx 1 \uf0de v2 \uf03d \uf0f2 v2\uf0a2dx \uf03d \uf0f2 cot xdx \uf03d ln sin x \u0e88\u0eb0\u0ec4\u0e94\u0ec9 yp \uf03d \uf02dx cos x \uf02b sin x \uf0d7 ln sin x \u0e94\u0ec8\u0eb1\u0e87\u0e99\u0e99\u0ec9\u0eb1 , \u0e9c\u0e99\u0ebb \u0eaa\u0eb0\u0ec0\u0ea5\u0ec8\u0e8d\u0e97\u0ec8\u0eb1\u0ebb\u0ea7\u0ec4\u0e9b\u0ec1\u0ea1\u0e99\u0ec8 y \uf03d yc \uf02b yp \uf03d c1 cos x \uf02b c2 sin x \uf02d x cos x \uf02b sin x \uf0d7 ln sin x 2. y\uf0a2\uf0a2 \uf02b y \uf03d cot x \u0ea7\u0e97\u0eb4 \u0ec1\u0eb5 \u0e81\u0ec9: \u0e8a\u0ead\u0e81\u0eab\u0eb3 yc \u0e88\u0eb3\u0e81\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99 y\uf0a2\uf0a2 \uf02b y \uf03d 0 \u0eaa\u0ea1\u0ebb \u0e9c\u0e99\u0ebb \u0e8a\u0ec8\u0ea7\u0e8d\u0ec1\u0ea1\u0ec8\u0e99 r2 \uf02b1 \uf03d 0 \uf0de r \uf03d \uf0b1i \u0eaa\u0eb0\u0e99\u0eb1\u0ec9\u0e99 yc \uf03d c1 cos x \uf02b c2 sin x \u0ec2\u0e94\u0e8d\u0e97\u0eb5 y1 \uf03d cos x \u0ec1\u0ea5\u0eb0 y2 \uf03d sin x \u0eaa\u0ebb\u0ea1\u0ea1\u0eb8\u0e94\u0e9c\u0ebb\u0e99\u0eaa\u0eb0\u0ec0\u0ea5\u0ec8\u0e8d\u0eaa\u0eb0\u0ec0\u0e9e\u0eb3\u0eb0\u0e84\u0eb7 yp \uf03d v1 cos x \uf02b v2 sin x \u0e81\u0eb3\u0e99\u0ebb\u0e94\u0ec0\u0e87\u0eb7\u0ead\u0e99\u0ec4\u0e82 \u0ec0\u0e9e\u0ead\u0eb5\u0eb7\u0ec8 \u0e88\u0eb0\u0eab\u0eb3\u0e84\u0eb3\u0ec8 v1 \u0ec1\u0ea5\u0eb0 v2 \u0e88\u0eb3\u0e81\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99\u0e94\u0ec8\u0e87\u0eb1 \u0e99\u0eb5:\u0ec9\u0eb1 \uf0ec\uf0efv1\uf0a2y1 \uf02b v2\uf0a2 y2 \uf03d 0 f (x) \uf0ed\uf0ef\uf0eev1\uf0a2y1\uf0a2 \uf02b v2\uf0a2 y2\uf0a2 a0 \uf03d \u0e88\u0eb3\u0e81 (D2 \uf02b1) y \uf03d cot x \u0e88\u0eb0\u0ec4\u0e94\u0ec9 f (x) \uf03d cot x , a0 \uf03d 1 \u0e88\u0eb0\u0ec4\u0e94\u0ec9\u0ea5\u0eb0\u0e9a\u0ebb\u0e9a\u0eaa\u0ebb\u0ea1\u0e9c\u0e99\u0ebb \uf0ee\uf0ed\uf0ecv\uf02d1\uf0a2vc1\uf0a2ossinxx\uf02b\uf02bv2v\uf0a2 2\uf0a2sicnosx \uf03d0 cot x x\uf03d \u0e8a\u0ead\u0e81\u0e84\u0ec8\u0eb3 v1, v2 \u0ec2\u0e94\u0e8d\u0ec3\u0e8a\u0e81\u0ec9 \u0e94\u0ebb \u0ec0\u0e81\u0e99\u0e81\u0ea3\u0eb3\u0ec0\u0ea1\u0eb5\u0e94\u0e87\u0ec8\u0eb1 \u0e99:\u0ec9\u0eb1\u0eb5 150","cos x sin x \uf03d cos2 x \uf02b sin2 x \uf03d 1 w\uf03d \uf02d sin x cos x 0 sin x v1\uf0a2 \uf03d cot x cos x \uf03d \uf02d cos x 1 \uf0de v1 \uf03d \uf0f2 v1\uf0a2dx \uf03d \uf02d\uf0f2 cos xdx \uf03d \uf02d sin x cos x 0 v2\uf0a2 \uf03d \uf02d sin x cot x \uf03d \uf028cos x\uf029\uf028cot x\uf029 \uf02d \uf028\uf02dsin x\uf029\uf0280\uf029 \uf03d cos2 x 1 sin x v2\uf0a2dx \uf03d cos2 x dx \uf03d 1\uf02d sin2 x sin x dx \uf0f2 \uf0f2 \uf0f2\uf0de v2 \uf03d sin x \uf03d \uf0f2 \uf0e6 1 x \uf02d sin x \uf0f6\uf0f7\uf0f8dx \uf03d ln cos ecx \uf02d cot x \uf02b cos x \uf0e7\uf0e8 sin \u0e88\u0eb0\u0ec4\u0e94\u0ec9 yp \uf03d \uf02d sin x cos x \uf02b \uf028ln cos ecx \uf02d cot x \uf02b cos x\uf029sin x \u0e94\u0ec8\u0eb1\u0e87\u0e99\u0e99\u0ec9\u0eb1 , \u0e9c\u0e99\u0ebb \u0eaa\u0eb0\u0ec0\u0ea5\u0e8d\u0ec8 \u0e97\u0ebb\u0ea7\u0ec8\u0eb1 \u0ec4\u0e9b\u0ec1\u0ea1\u0ec8\u0e99 y \uf03d yc \uf02b yp y \uf03d c1 cos x \uf02b c2 sin x \uf02d sin x cos x \uf02b \uf028ln cos ecx \uf02d cot x \uf02b cos x\uf029sin x 3. (D2 \uf02b1) y \uf03d sec x tan x \u0ea7\u0e97\u0eb4 \u0ec1\u0eb5 \u0e81:\u0ec9 \u0e8a\u0ead\u0e81\u0eab\u0eb3 yc \u0e88\u0eb3\u0e81\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99 y\uf0a2\uf0a2 \uf02b y \uf03d 0 \u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99\u0e8a\u0ec8\u0ea7\u0e8d\u0ec1\u0ea1\u0e99\u0ec8 r2 \uf02b1 \uf03d 0 \uf0de r \uf03d \uf0b1i \u0eaa\u0eb0\u0e99\u0ec9\u0e99\u0eb1 yc \uf03d c1 cos x \uf02b c2 sin x \u0ec2\u0e94\u0e8d\u0e97\u0eb5 y1 \uf03d cos x \u0ec1\u0ea5\u0eb0 y2 \uf03d sin x \u0eaa\u0ebb\u0ea1\u0ea1\u0eb8\u0e94\u0e9c\u0ebb\u0e99\u0eaa\u0eb0\u0ec0\u0ea5\u0ec8\u0e8d\u0eaa\u0eb0\u0ec0\u0e9e\u0eb3\u0eb0\u0e84\u0eb7 yp \uf03d v1 cos x \uf02b v2 sin x \u0e81\u0eb3\u0e99\u0e94\u0ebb \u0ec0\u0e87\u0eb7\u0ead\u0e99\u0ec4\u0e82 \u0ec0\u0e9e\u0ec8\u0eb7\u0ead\u0eb5 \u0e88\u0eb0\u0eab\u0eb3\u0e84\u0ec8\u0eb3 v1 \u0ec1\u0ea5\u0eb0 v2 \u0e88\u0eb3\u0e81\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99\u0e94\u0e87\u0eb1\u0ec8 \u0e99:\u0ec9\u0eb5\u0eb1 \uf0ec\uf0efv1\uf0a2y1 \uf02b v2\uf0a2 y2 \uf03d 0 f (x) \uf0ee\uf0ed\uf0efv1\uf0a2y1\uf0a2 \uf02b v2\uf0a2 y2\uf0a2 a0 \uf03d \u0e88\u0eb3\u0e81 (D2 \uf02b1) y \uf03d sec x tan x \u0e88\u0eb0\u0ec4\u0e94\u0ec9 f (x) \uf03d sec x tan x , a0 \uf03d 1 \u0e88\u0eb0\u0ec4\u0e94\u0ea5\u0ec9 \u0eb0\u0e9a\u0ebb\u0e9a\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99 \uf0ed\uf0ec\uf0eev\uf02d1\uf0a2vc1\uf0a2ossinxx\uf02b\uf02bv2v\uf0a2 2\uf0a2sicnosx \uf03d0 sec x tan x x\uf03d \u0e8a\u0ead\u0e81\u0e84\u0eb3\u0ec8 v1, v2 \u0ec2\u0e94\u0e8d\u0ec3\u0e8a\u0e81\u0ec9 \u0e94\u0ebb \u0ec0\u0e81\u0e99\u0e81\u0ea3\u0eb3\u0ec0\u0ea1\u0e94\u0eb5 \u0e87\u0ec8\u0eb1 \u0e99\u0eb1:\u0eb5\u0ec9 151","cos x sin x \uf03d cos2 x \uf02b sin2 x \uf03d 1 w\uf03d \uf02d sin x cos x 0 sin x v1\uf0a2 \uf03d sec x tan x cos x \uf03d \uf02d sin x sec x tan x \uf03d \uf02d tan2 x 1 v1\uf0a2dx \uf03d \uf02d tan2 x dx \uf03d \uf02d sin 2 x \uf0f2 \uf0f2 \uf0f2\uf0de v1 \uf03d cos2 x dx \uf0e6 1 \uf02d cos2 x \uf0f6 \uf0e6 1 \uf02d1\uf0f8\uf0f6\uf0f7dx \uf0e7 cos2 x \uf0f7dx \uf0e7\uf0e8 cos2 \uf0f2 \uf0f2\uf03d \uf02d\uf0e8 \uf0f8 \uf03d \uf02d x \uf03d \uf02d\uf028tan x \uf02d x\uf029 \uf03d \uf02d tan x \uf02b x cos x 0 v2\uf0a2 \uf03d \uf02d sin x sec x tan x \uf03d \uf028cos x\uf029\uf028sec x tan x\uf029 \uf02d \uf028\uf02dsin x\uf029\uf0280\uf029 \uf03d tan x 1 \uf0de v2 \uf03d \uf0f2 v2\uf0a2dx \uf03d \uf0f2 tan xdx \uf03d ln sec x \u0e88\u0eb0\u0ec4\u0e94\u0ec9 yp \uf03d \uf028 x \uf02d tan x\uf029 cos x \uf02b \uf028ln sec x \uf029sin x \u0e94\u0e87\u0ec8\u0eb1 \u0e99\u0ec9\u0e99\u0eb1 , \u0e9c\u0e99\u0ebb \u0eaa\u0eb0\u0ec0\u0ea5\u0ec8\u0e8d\u0e97\u0eb1\u0ebb\u0ec8\u0ea7\u0ec4\u0e9b\u0ec1\u0ea1\u0ec8\u0e99 y \uf03d yc \uf02b yp y \uf03d c1 cos x \uf02b c2 sin x \uf02b \uf028 x \uf02d tan x\uf029 cos x \uf02b \uf028ln sec x \uf029sin x 4. (D2 \uf02b 4D \uf02b 5) y \uf03d e\uf02d2x sec x \u0ea7\u0e97\u0eb4 \u0ec1\u0eb5 \u0e81\u0ec9: \u0e8a\u0ead\u0e81\u0eab\u0eb3 yc \u0e88\u0eb3\u0e81\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99 (D2 \uf02b 4D \uf02b 5) y \uf03d 0 \u0eaa\u0ea1\u0ebb \u0e9c\u0ebb\u0e99\u0e8a\u0ec8\u0ea7\u0e8d\u0ec1\u0ea1\u0e99\u0ec8 r2 \uf02b 4r \uf02b 5 \uf03d 0 \u0e99\u0eb3\u0ec3\u0e8a\u0ec9\u0eaa\u0e94\u0eb9 ar2 \uf02b br \uf02b c \uf03d 0 \u0e88\u0eb0\u0ec4\u0e94\u0ec9 r \uf03d \uf02db \uf0b1 b2 \uf02d 4ac 2a \u0e88\u0eb3\u0e81 r2 \uf02b 4r \uf02b 5 \uf03d 0 \u0e88\u0eb0\u0ec4\u0e94\u0ec9 \uf02d4 \uf0b1 42 \uf02d 4\uf0281\uf029\uf0285\uf029 \uf03d \uf02d4 \uf0b1 \uf02d4 \uf03d \uf02d4 \uf0b1 2i \uf03d \uf02d2 \uf0b1 i r\uf03d 2\uf0281\uf029 2 2 \u0eaa\u0eb0\u0e99\u0eb1\u0ec9\u0e99 yc \uf03d e\uf02d2x \uf028c1 cos x \uf02b c2 sin x\uf029 \uf03d c1e\uf02d2x cos x \uf02b c2e\uf02d2x sin x \u0ec2\u0e94\u0e8d\u0e97\u0eb5 y1 \uf03d e\uf02d2x cos x \u0ec1\u0ea5\u0eb0 y2 \uf03d e\uf02d2x sin x \u0eaa\u0ebb\u0ea1\u0ea1\u0eb8\u0e94\u0e9c\u0ebb\u0e99\u0eaa\u0eb0\u0ec0\u0ea5\u0e8d\u0ec8 \u0eaa\u0eb0\u0ec0\u0e9e\u0eb3\u0eb0\u0e84\u0eb7 yp \uf03d v1e\uf02d2x cos x \uf02b v2e\uf02d2x sin x \u0e81\u0eb3\u0e99\u0e94\u0ebb \u0ec0\u0e87\u0ead\u0eb7 \u0e99\u0ec4\u0e82 \u0ec0\u0e9e\u0ec8\u0eb7\u0eb5\u0ead\u0e88\u0eb0\u0eab\u0eb3\u0e84\u0eb3\u0ec8 v1 \u0ec1\u0ea5\u0eb0 v2 \u0e88\u0eb3\u0e81\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99\u0e94\u0eb1\u0ec8\u0e87\u0e99\u0eb1\u0ec9:\u0eb5 \uf0ec\uf0efv1\uf0a2y1 \uf02b v2\uf0a2 y2 \uf03d 0 f (x) \uf0ee\uf0ef\uf0edv1\uf0a2y1\uf0a2 \uf02b v2\uf0a2 y2\uf0a2 a0 \uf03d \u0e88\u0eb3\u0e81 (D2 \uf02b 4D \uf02b 5) y \uf03d e\uf02d2x sec x \u0e88\u0eb0\u0ec4\u0e94\u0ec9 f (x) \uf03d e\uf02d2x sec x, a0 \uf03d 1 152","\uf0ef\uf0ecv1\uf0a2e\uf02d2x cos x \uf02b v2\uf0a2e\uf02d2x sin x \uf03d 0 \uf0ef\uf0ee\uf0edv1\uf0a2 \uf02d2e\uf02d2x cos x \uf02d e\uf02d2x sin x \uf02b v2\uf0a2 e\uf02d2x cos x \uf02d 2e\uf02d2x sin x \uf03d e\uf02d2x sec x \uf028 \uf029 \uf028 \uf029\u0e88\u0eb0\u0ec4\u0e94\u0ea5\u0ec9 \u0eb0\u0e9a\u0ebb\u0e9a\u0eaa\u0ebb\u0ea1\u0e9c\u0e99\u0ebb \u0e8a\u0ead\u0e81\u0e84\u0eb3\u0ec8 v1, v2 \u0ec2\u0e94\u0e8d\u0ec3\u0e8a\u0ec9\u0e81\u0e94\u0ebb \u0ec0\u0e81\u0e99\u0e81\u0ea3\u0eb3\u0ec0\u0ea1\u0eb5\u0e94\u0e87\u0eb1\u0ec8 \u0e99\u0eb5\u0eb1\u0ec9: e\uf02d2x cos x e\uf02d2x sin x w\uf03d e\uf02d2x cos x \uf02d 2e\uf02d2x sin x \uf02d 2e\uf02d2x cos x \uf02d e\uf02d2x sin x \uf028 \uf029\uf028 \uf029 \uf028 \uf029\uf028 \uf029\uf03d e\uf02d2x cos x e\uf02d2x cos x \uf02d 2e\uf02d2x sin x \uf02d e\uf02d2x sin x \uf02d2e\uf02d2x cos x \uf02d e\uf02d2x sin x \uf028 \uf029 \uf028 \uf029\uf03d e\uf02d4x cos2 x \uf02d 2e\uf02d4x cos x sin x \uf02d \uf02d2e\uf02d4x cos x sin x \uf02d e\uf02d4x sin2 x \uf03d e\uf02d4x cos2 x \uf02b e\uf02d4x sin2 x \uf03d e\uf02d4x 0 e\uf02d2x sin x v1\uf0a2 \uf03d e\uf02d2x sec x e\uf02d2x cos x \uf02d 2e\uf02d2x sin x \uf03d \uf02de\uf02d4 x sec x sin x e\uf02d4 x e\uf02d4 x \uf03d \uf02d sec x sin x \uf03d \uf02d sin x \uf03d \uf02d tan x cos x \uf0de v1 \uf03d \uf0f2 v1\uf0a2dx \uf03d \uf02d\uf0f2 tan xdx \uf03d ln cos x e\uf02d2x cos x 0 v2\uf0a2 \uf03d e\uf02d2x cos x \uf02d 2e\uf02d2x sin x e\uf02d2x sec x \uf03d e\uf02d4 x cos x sec x e\uf02d4 x e\uf02d4 x \uf03d cos x sec x \uf03d 1 \uf0de v2 \uf03d \uf0f2 v2\uf0a2dx \uf03d \uf0f21dx \uf03d x \uf028 \uf029\u0e88\u0eb0\u0ec4\u0e94\u0ec9 yp \uf03d ln cos x e\uf02d2x cos x \uf02b xe\uf02d2x sin x \u0e94\u0eb1\u0e87\u0ec8 \u0e99\u0ec9\u0eb1\u0e99,\u0e9c\u0e99\u0ebb \u0eaa\u0eb0\u0ec0\u0ea5\u0e8d\u0ec8 \u0e97\u0ec8\u0ea7\u0eb1\u0ebb \u0ec4\u0e9b\u0ec1\u0ea1\u0e99\u0ec8 y \uf03d yc \uf02b yp \uf028 \uf029y \uf03d c1e\uf02d2x cos x \uf02b c2e\uf02d2x sin x \uf02b ln cos x e\uf02d2x cos x \uf02b xe\uf02d2x sin x 5. y\uf0a2\uf0a2 \uf02b y \uf03d sec3 x \u0ea7\u0e97\u0eb4 \u0ec1\u0eb5 \u0e81:\u0ec9 \u0e8a\u0ead\u0e81\u0eab\u0eb3 yc \u0e88\u0eb3\u0e81\u0eaa\u0ea1\u0ebb \u0e9c\u0ebb\u0e99 y\uf0a2\uf0a2 \uf02b y \uf03d 0 \u0eaa\u0ea1\u0ebb \u0e9c\u0ebb\u0e99\u0e8a\u0ec8\u0ea7\u0e8d\u0ec1\u0ea1\u0e99\u0ec8 r2 \uf02b1 \uf03d 0 \uf0de r \uf03d \uf0b1i \u0eaa\u0eb0\u0e99\u0e99\u0ec9\u0eb1 yc \uf03d c1 cos x \uf02b c2 sin x \u0ec2\u0e94\u0e8d\u0e97\u0eb5 y1 \uf03d cos x \u0ec1\u0ea5\u0eb0 y2 \uf03d sin x \uf0ef\uf0ecv1\uf0a2y1 \uf02b v2\uf0a2 y2 \uf03d 0 f (x) \u0eaa\u0ebb\u0ea1\u0ea1\u0eb8\u0e94\u0e9c\u0e99\u0ebb \u0eaa\u0eb0\u0ec0\u0ea5\u0ec8\u0e8d\u0eaa\u0eb0\u0ec0\u0e9e\u0eb3\u0eb0\u0e84\u0eb7 yp \uf03d v1 cos x \uf02b v2 sin x \uf0ed\uf0ef\uf0eev1\uf0a2y1\uf0a2 \uf02b v2\uf0a2 y2\uf0a2 a0 \uf03d \u0e81\u0eb3\u0e99\u0e94\u0ebb \u0ec0\u0e87\u0ead\u0eb7 \u0e99\u0ec4\u0e82 \u0ec0\u0e9e\u0eb5\u0ead\u0ec8\u0eb7 \u0e88\u0eb0\u0eab\u0eb3\u0e84\u0ec8\u0eb3 v1 \u0ec1\u0ea5\u0eb0 v2 \u0e88\u0eb3\u0e81\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99\u0e94\u0e87\u0eb1\u0ec8 \u0e99\u0eb5\u0eb1\u0ec9: \u0e88\u0eb3\u0e81 y\uf0a2\uf0a2 \uf02b y \uf03d sec3 x \u0e88\u0eb0\u0ec4\u0e94\u0ec9 f (x) \uf03d sec3 x, a0 \uf03d1 153","\u0e88\u0eb0\u0ec4\u0e94\u0ea5\u0ec9 \u0eb0\u0e9a\u0e9a\u0ebb \u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99 \uf0ef\uf0ef\uf0ed\uf0ee\uf0ecv\uf02d1\uf0a2vc1\uf0a2ossinxx\uf02b\uf02bvv2\uf0a2 2\uf0a2sicnoxs \uf03d0 x x \uf03d sec3 \u0e8a\u0ead\u0e81\u0e84\u0eb3\u0ec8 v1, v2 \u0ec2\u0e94\u0e8d\u0ec3\u0e8a\u0ec9\u0e81\u0e94\u0ebb \u0ec0\u0e81\u0e99\u0e81\u0ea3\u0eb3\u0ec0\u0ea1\u0e94\u0eb5 \u0e87\u0eb1\u0ec8 \u0e99\u0eb1\u0eb5\u0ec9: cos x sin x \uf03d cos2 x \uf02b sin2 x \uf03d 1 w\uf03d \uf02d sin x cos x 0 sin x v1\uf0a2 \uf03d sec3 x cos x \uf03d \uf02d sin x sec3 x \uf03d \uf02d sin x cos3 x 1 \uf0de v1 \uf03d \uf0f2 v1\uf0a2dx \uf03d \uf02d\uf0f2 sin x dx \uf03d \uf0f2 cos\uf02d3 xd \uf028cos x\uf029 cos3 x \uf03d\uf02d 1 2 cos2 x cos x 0 \uf02dsin x sec3 x 1 1 cos2 \uf028 \uf029v2\uf0a2 \uf03d \uf03d \uf028cos x\uf029 sec3 x \uf02d \uf028\uf02d sin x \uf029 \uf0280\uf029 \uf03d x v2\uf0a2dx \uf03d 1 dx \uf03d tan x \uf0f2 \uf0f2\uf0de v2 \uf03d cos2 x \u0e88\u0eb0\u0ec4\u0e94\u0ec9 yp \uf03d \uf02d 1 x cos x \uf02b tan x sin x \uf03d \uf02d 1 x \uf02b tan x sin x 2 cos2 2 cos \u0e94\u0eb1\u0e87\u0ec8 \u0e99\u0ec9\u0e99\u0eb1 ,\u0e9c\u0e99\u0ebb \u0eaa\u0eb0\u0ec0\u0ea5\u0e8d\u0ec8 \u0e97\u0ebb\u0ea7\u0ec8\u0eb1 \u0ec4\u0e9b\u0ec1\u0ea1\u0ec8\u0e99 y \uf03d yc \uf02b yp \uf03d c1 cos x \uf02b c2 sin x \uf02d 1 x \uf02b tan x sin x 2 cos 6. y\uf0a2\uf0a2 \uf02d 3 y\uf0a2 \uf02b 2 y \uf03d 1 1 x \uf02b e\uf02d \u0ea7\u0e97\u0eb4 \u0ec1\u0eb5 \u0e81:\u0ec9 \u0e8a\u0ead\u0e81\u0eab\u0eb3 yc \u0e88\u0eb3\u0e81\u0eaa\u0ea1\u0ebb \u0e9c\u0ebb\u0e99 y\uf0a2\uf0a2 \uf02d 3y\uf0a2 \uf02b 2y \uf03d 0 \u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99\u0e8a\u0ea7\u0ec8 \u0e8d\u0ec1\u0ea1\u0e99\u0ec8 r2 \uf02d 3r \uf02b 2 \uf03d 0 (r \uf02d1)(r \uf02d 2) \uf03d 0 r \uf03d 1; 2 \u0eaa\u0eb0\u0e99\u0ec9\u0e99\u0eb1 yc \uf03d c1ex \uf02b c2e2x \u0ec2\u0e94\u0e8d\u0e97\u0eb5\u0ec8 y1 \uf03d ex \u0ec1\u0ea5\u0eb0 y2 \uf03d e2x \u0eaa\u0ebb\u0ea1\u0ea1\u0eb8\u0e94\u0e9c\u0ebb\u0e99\u0eaa\u0eb0\u0ec0\u0ea5\u0e8d\u0ec8 \u0eaa\u0eb0\u0ec0\u0e9e\u0eb3\u0eb0\u0e84\u0eb7 yp \uf03d v1ex \uf02b v2e2x \u0e81\u0eb3\u0e99\u0ebb\u0e94\u0ec0\u0e87\u0eb7\u0ead\u0e99\u0ec4\u0e82 \u0ec0\u0e9e\u0ec8\u0ead\u0eb7\u0eb5 \u0e88\u0eb0\u0eab\u0eb3\u0e84\u0ec8\u0eb3 v1 \u0ec1\u0ea5\u0eb0 v2 \u0e88\u0eb3\u0e81\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99\u0e94\u0eb1\u0e87\u0ec8 \u0e99\u0eb5\u0eb1\u0ec9: \uf0ec\uf0efv1\uf0a2y1 \uf02b v2\uf0a2 y2 \uf03d 0 f (x) \uf0ee\uf0ef\uf0edv1\uf0a2y1\uf0a2 \uf02b v2\uf0a2 y2\uf0a2 a0 \uf03d \u0e88\u0eb3\u0e81 y\uf0a2\uf0a2 \uf02d 3y\uf0a2 \uf02b 2 y \uf03d 1 \u0e88\u0eb0\u0ec4\u0e94\u0ec9 f (x) \uf03d 1 , a0 \uf03d1 1\uf02b e\uf02dx 1\uf02b e\uf02dx 154","\u0e88\u0eb0\u0ec4\u0e94\u0ec9\u0ea5\u0eb0\u0e9a\u0ebb\u0e9a\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99 \uf0ec\uf0efv1\uf0a2ex \uf02b v2\uf0a2e2x \uf03d 0 \uf0ed\uf0ef\uf0eev1\uf0a2ex 1 \uf02b 2v2\uf0a2e2x \uf03d 1 \uf02b e\uf02d x \u0e8a\u0ead\u0e81\u0e84\u0eb3\u0ec8 v1, v2 \u0ec2\u0e94\u0e8d\u0ec3\u0e8a\u0e81\u0ec9 \u0ebb\u0e94\u0ec0\u0e81\u0e99\u0e81\u0ea3\u0eb3\u0ec0\u0ea1\u0eb5\u0e94\u0ec8\u0eb1\u0e87\u0e99:\u0eb1\u0eb5\u0ec9 ex e2x \uf03d 2e3x \uf02d e3x \uf03d e3x w\uf03d ex 2e2x 0 e2x 1 2ex \uf02d e2x \uf02b e\uf02d v1\uf0a2 \uf03d 1\uf02b e\uf02dx \uf03d 1 x \uf03d \uf02d e\uf02dx e3x \uf02b e\uf02d e3x 1 x v1\uf0a2dx \uf03d \uf02d e\uf02dx e\uf02d x \uf0f2 \uf0f2\uf0de v1 \uf03d 1\uf02b e\uf02d dx \uf03d ln 1\uf02b x ex 0 ex 1 ex v2\uf0a2 \uf03d 1\uf02b e\uf02dx \uf03d 1\uf02b e\uf02dx \uf03d 1 e\uf02d2 x x e3x e3x \uf02b e\uf02d v2\uf0a2dx \uf03d e\uf02d2 x \uf0e6 e\uf02dx e\uf02dx \uf0f6 1\uf02b e\uf02dx \uf0e7 1\uf02b e\uf02dx \uf0f7dx \uf0f2 \uf0f2 \uf0f2\uf0de v2 \uf03d dx \uf03d \uf0e8 \uf02d \uf0f8 \uf03d \uf02de\uf02dx \uf02b ln 1\uf02b e\uf02dx \uf028 \uf029\u0e88\u0eb0\u0ec4\u0e94\u0ec9 yp \uf03d ex ln 1\uf02b e\uf02dx \uf02b \uf02de\uf02dx \uf02b ln 1\uf02b e\uf02dx e2x \uf03d ex ln 1\uf02b e\uf02dx \uf02d ex \uf02b e2x ln 1\uf02b e\uf02dx \u0e94\u0ec8\u0eb1\u0e87\u0e99\u0eb1\u0e99\u0ec9 ,\u0e9c\u0ebb\u0e99\u0eaa\u0eb0\u0ec0\u0ea5\u0e8d\u0ec8 \u0e97\u0eb1\u0ec8\u0ebb\u0ea7\u0ec4\u0e9b\u0ec1\u0ea1\u0e99\u0ec8 y \uf03d yc \uf02b yp y \uf03d c1ex \uf02b c2e2x \uf02b ex ln 1\uf02b e\uf02dx \uf02d ex \uf02b e2x ln 1\uf02b e\uf02dx y \uf03d c1ex \uf02b c2e2x \uf02b ex ln 1\uf02b e\uf02dx \uf02b e2x ln 1\uf02b e\uf02dx \u0ec2\u0e94\u0e8d\u0e97\u0eb5\u0ec8 c1ex \u0eae\u0ec8\u0ea7\u0ea1\u0e81\u0e9a \uf02dex 7. (D2 \uf02b 3D \uf02b 2) y \uf03d 1 1\uf02b ex \u0ea7\u0e97\u0eb4 \u0ec1\u0eb5 \u0e81:\u0ec9 \u0e8a\u0ead\u0e81\u0eab\u0eb3 yc \u0e88\u0eb3\u0e81\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99 (D2 \uf02b 3D \uf02b 2) y \uf03d 0 \u0eaa\u0ebb\u0ea1\u0e9c\u0e99\u0ebb \u0e8a\u0ea7\u0ec8 \u0e8d\u0ec1\u0ea1\u0ec8\u0e99 r2 \uf02b 3r \uf02b 2 \uf03d 0 (r \uf02b1)(r \uf02b 2) \uf03d 0 \uf0de r \uf03d \uf02d1; \uf02d2 \u0eaa\u0eb0\u0e99\u0eb1\u0e99\u0ec9 yc \uf03d c1e\uf02dx \uf02b c2e\uf02d2x \u0ec2\u0e94\u0e8d\u0e97\u0eb5\u0ec8 y1 \uf03d e\uf02dx \u0ec1\u0ea5\u0eb0 y2 \uf03d e\uf02d2x \u0eaa\u0ea1\u0ebb \u0ea1\u0eb8\u0e94\u0e9c\u0e99\u0ebb \u0eaa\u0eb0\u0ec0\u0ea5\u0e8d\u0ec8 \u0eaa\u0eb0\u0ec0\u0e9e\u0eb3\u0eb0\u0e84\u0eb7 yp \uf03d v1e\uf02dx \uf02b v2e\uf02d2x \u0e81\u0eb3\u0e99\u0ebb\u0e94\u0ec0\u0e87\u0ead\u0eb7 \u0e99\u0ec4\u0e82 \u0ec0\u0e9e\u0eb5\u0ec8\u0eb7\u0ead\u0e88\u0eb0\u0eab\u0eb3\u0e84\u0ec8\u0eb3 v1 \u0ec1\u0ea5\u0eb0 v2 \u0e88\u0eb3\u0e81\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99\u0e94\u0ec8\u0e87\u0eb1 \u0e99:\u0eb5\u0ec9\u0eb1 155","\uf0ef\uf0ecv1\uf0a2y1 \uf02b v2\uf0a2 y2 \uf03d 0 f (x) \uf0ef\uf0ee\uf0edv1\uf0a2y1\uf0a2 \uf02b v2\uf0a2 y2\uf0a2 a0 \uf03d \u0e88\u0eb3\u0e81 (D2 \uf02d 3D \uf02b 2) y \uf03d 1 \u0e88\u0eb0\u0ec4\u0e94\u0ec9 f (x) \uf03d 1 , a0 \uf03d1 1\uf02b ex 1\uf02b ex \u0e88\u0eb0\u0ec4\u0e94\u0ec9\u0ea5\u0eb0\u0e9a\u0e9a\u0ebb \u0eaa\u0ebb\u0ea1\u0e9c\u0e99\u0ebb \uf0ef\uf0ecv1\uf0a2e\uf02dx \uf02b v2\uf0a2e\uf02d2x \uf03d 0 \uf0ed\uf0ee\uf0ef\uf02dv1\uf0a2e\uf02d x 1 \uf02d 2v\uf0a2e\uf02d2 x \uf03d 1\uf02b ex 2 \u0e8a\u0ead\u0e81\u0e84\u0ec8\u0eb3 v1, v2 \u0ec2\u0e94\u0e8d\u0ec3\u0e8a\u0ec9\u0e81\u0ebb\u0e94\u0ec0\u0e81\u0e99\u0e81\u0ea3\u0eb3\u0ec0\u0ea1\u0e94\u0eb5 \u0ec8\u0e87\u0eb1 \u0e99\u0ec9\u0eb5:\u0eb1 e\uf02dx e\uf02d2x \uf03d \uf02d2e\uf02d3x \uf02b e\uf02d3x \uf03d \uf02de\uf02d3x w\uf03d \uf02de\uf02dx \uf02d 2e\uf02d2x 0 e\uf02d2x 1 \uf02d 2e\uf02d2x \uf02d e\uf02d2 x \uf03d \uf02d ex v1\uf0a2 \uf03d 1\uf02b ex e\uf02d3x 1\uf02b ex 1\uf02b ex \uf03d e\uf02d3x v1\uf0a2dx \uf03d e x x \uf0f2 \uf0f2\uf0de v1 \uf03d \uf02b dx \uf03d ln 1 \uf02b e 1 e x e\uf02dx 0 \uf02de\uf02d x 1 e\uf02dx 1\uf02b ex v2\uf0a2 \uf03d \uf03d 1\uf02b ex \uf03d e2x e \uf02d3 x e\uf02d3x 1\uf02b ex v2\uf0a2dx \uf03d e2x dx \uf03d \uf0e6 ex ex \uf0f6 1\uf02b ex \uf0e7 1\uf02b ex \uf0f7dx \uf0f2 \uf0f2 \uf0f2\uf0de v2 \uf03d \uf0e8 \uf02d \uf0f8 \uf03d ex \uf02d ln 1\uf02b ex \u0e88\u0eb0\u0ec4\u0e94\u0ec9 \uf028 \uf029 \uf028 \uf029yp \uf03d ln 1\uf02b ex e\uf02dx \uf02b ex \uf02d ln 1\uf02b ex e\uf02d2x \uf03d e\uf02dx ln 1\uf02b ex \uf02b e\uf02dx \uf02d e\uf02d2x ln 1\uf02b ex \u0e94\u0ec8\u0eb1\u0e87\u0e99\u0e99\u0ec9\u0eb1 ,\u0e9c\u0ebb\u0e99\u0eaa\u0eb0\u0ec0\u0ea5\u0e8d\u0ec8 \u0e97\u0ec8\u0ea7\u0eb1\u0ebb \u0ec4\u0e9b\u0ec1\u0ea1\u0ec8\u0e99 y \uf03d yc \uf02b yp y \uf03d c1e\uf02dx \uf02b c2e\uf02d2x \uf02b e\uf02dx ln 1\uf02b ex \uf02b e\uf02dx \uf02d e\uf02d2x ln 1\uf02b ex y \uf03d c1e\uf02dx \uf02b c2e\uf02d2x \uf02b e\uf02dx ln 1\uf02b ex \uf02d e\uf02d2x ln 1\uf02b ex \u0ec2\u0e94\u0e8d\u0e97\u0eb5\u0ec8 c1e\uf02dx \u0eae\u0ec8\u0ea7\u0ea1\u0e81\u0e9a e\uf02dx 8. (D3 \uf02b D) y \uf03d tan x \u0ea7\u0e97\u0eb4 \u0ec1\u0eb5 \u0e81:\u0ec9 \u0e8a\u0ead\u0e81\u0eab\u0eb3 yc \u0e88\u0eb3\u0e81\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99 (D3 \uf02b D) y \uf03d 0 \u0eaa\u0ebb\u0ea1\u0e9c\u0e99\u0ebb \u0e8a\u0ea7\u0ec8 \u0e8d\u0ec1\u0ea1\u0e99\u0ec8 r3 \uf02b r \uf03d 0 r(r2 \uf02b1) \uf03d 0 \uf0de r \uf03d 0; \uf0b1i 156","\u0eaa\u0eb0\u0e99\u0eb1\u0e99\u0ec9 yp \uf03d v1 \uf02b v2 cos x \uf02b v3 sin x \u0ec2\u0e94\u0e8d\u0e97\u0eb5\u0ec8 y1 \uf03d 1; y2 \uf03d cos x \u0ec1\u0ea5\u0eb0 y3 \uf03d sin x \u0eaa\u0ea1\u0ebb \u0ea1\u0eb8\u0e94\u0e9c\u0e99\u0ebb \u0eaa\u0eb0\u0ec0\u0ea5\u0ec8\u0e8d\u0eaa\u0eb0\u0ec0\u0e9e\u0eb3\u0eb0\u0e84\u0ec8\u0eb5\u0eb7: yp \uf03d v1 \uf02b v2 cos x \uf02b v3 sin x \u0e81\u0eb3\u0e99\u0e94\u0ebb \u0ec0\u0e87\u0ec8\u0ead\u0eb7\u0eb5 \u0e99\u0ec4\u0e82\u0ec0\u0e9e\u0eb7\u0ec8\u0eb5\u0ead\u0e88\u0eb0\u0eab\u0eb3\u0e84\u0ec8\u0eb3\u0e82\u0ead\u0e87 v1, v2, v3 \u0e88\u0eb3\u0e81\u0ea5\u0eb0\u0e9a\u0e9a\u0ebb \u0eaa\u0ebb\u0ea1\u0e9c\u0e99\u0ebb \u0e94\u0e87\u0ec8\u0eb1 \u0e99\u0ec9\u0eb1\u0eb5: \uf0ec \uf0ef\uf0ef\uf0ef\uf0edvv11\uf0a2\uf0a2 y1 \uf02b v2\uf0a2 y2 \uf02b v3\uf0a2 y3 \uf03d 0 y1\uf0a2 \uf02b v2\uf0a2 y2\uf0a2 \uf02b v3\uf0a2 y3\uf0a2 \uf03d 0 \uf0ef f (x) \uf0ef\uf0ef\uf0eev1\uf0a2y1\uf0a2\uf0a2\uf02b v2\uf0a2 y2\uf0a2\uf0a2 \uf02b v3\uf0a2 y3\uf0a2\uf0a2 \uf03d a0 \u0e88\u0eb3\u0e81 (D3 \uf02b D) y \uf03d tan x \u0e88\u0eb0\u0ec4\u0e94\u0ec9 f (x) \uf03d tan x, a 0 \uf03d 1 \u0e88\u0eb0\u0ec4\u0e94\u0ea5\u0ec9 \u0eb0\u0e9a\u0ebb\u0e9a\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99 \uf0ec\uf0efv1\uf0a2 \uf02b v2\uf0a2 cos x \uf02b v3\uf0a2 sin x \uf03d 0 \uf0ed \uf02d v2\uf0a2 sin x \uf02b v3\uf0a2 cos x \uf03d 0 \uf0ee\uf0ef \uf02d v2\uf0a2 cos x \uf02d v3\uf0a2 sin x \uf03d tan x \u0e8a\u0ead\u0e81\u0eab\u0eb3\u0e84\u0eb3\u0ec8 \u0e82\u0ead\u0e87 v1, v2, v3 \u0ec2\u0e94\u0e8d\u0e81\u0eb3\u0e99\u0e99\u0eb3\u0ec3\u0e8a\u0e81\u0ec9 \u0e94\u0ebb \u0e82\u0ead\u0e87\u0e81\u0ea3\u0eb3\u0ec0\u0ea1\u0eb5\u0e94\u0eb1\u0e87\u0ec8 \u0e99\u0eb1\u0eb5:\u0ec9 1 cos x sin x w \uf03d 0 \uf02d sin x cos x \uf03d sin2 x \uf02b cos2 x \uf03d 1 o \uf02d cos x \uf02d sin x 0 cos x sin x 0 \uf02d sin x cos x \uf02d cos x \uf02d sin x \uf03d \uf028tan x\uf029 cos2 x \uf02b sin2 x \uf03d tan x 1 \uf028 \uf029v1\uf0a2 \uf03d tan x \uf0de v1 \uf03d \uf0f2 v1\uf0a2dx \uf03d \uf0f2 tan xdx \uf03d \uf0f2 sin x dx \uf03d \uf02d\uf0f2 1 d (cos x) \uf03d \uf02d ln cos x cos x cos x 10 sin x 00 cos x v2\uf0a2 \uf03d 0 tan x \uf02d sin x \uf03d \uf02d tan x cos x \uf03d \uf02d sin x 1 \uf0de v2 \uf03d \uf0f2 v2\uf0a2dx \uf03d \uf02d\uf0f2 sin xdx \uf03d cos x 1 cos x 0 0 \uf02d sin x 0 v3\uf0a2 \uf03d 0 \uf02d cos x tan x \uf03d \uf02d tan x sin x \uf03d \uf02d sin2 x 1 cos x v3\uf0a2dx \uf03d \uf02d sin2 x dx \uf03d \uf02d 1\uf02d cos2 xdx cos x cos x \uf0f2 \uf0f2 \uf0f2\uf0de v3 \uf03d \uf03d \uf02d\uf0f2 \uf0e6 1 x \uf02d cos x \uf0f8\uf0f7\uf0f6dx \uf03d \uf02d ln sec x \uf02b tan x \uf02b sin x \uf0e8\uf0e7 cos 157","\u0e88\u0eb0\u0ec4\u0e94\u0ec9 yp \uf03d \uf02d ln cos x \uf02b \uf028cos x\uf029cos x \uf02b \uf028\uf02d ln sec x \uf02b tan x \uf02b sin x\uf029sin x \uf03d \uf02d ln cos x \uf02b cos2 x \uf02d sin x ln sec x \uf02b tan x \uf02b sin2 x \uf03d \uf02d ln cos x \uf02d sin x ln sec x \uf02b tan x \u0e94\u0e87\u0ec8\u0eb1 \u0e99\u0e99\u0ec9\u0eb1 , \u0e9c\u0ebb\u0e99\u0eaa\u0eb0\u0ec0\u0ea5\u0ec8\u0e8d\u0e97\u0ec8\u0ea7\u0eb1\u0ebb \u0ec4\u0e9b\u0ec1\u0ea1\u0e99\u0ec8 y \uf03d yc \uf02b yp y \uf03d v1 \uf02b v2 cos x \uf02b v3 sin x \uf02d ln cos x \uf02d sin x ln sec x \uf02b tan x 9. (D3 \uf02b 3D2 \uf02b 3D \uf02b1) y \uf03d ex 3 \u0ea7\u0e97\u0eb4 \u0ec1\u0eb5 \u0e81:\u0ec9 \u0e8a\u0ead\u0e81\u0eab\u0eb3 yc \u0e88\u0eb3\u0e81\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99 (D3 \uf02b 3D2 \uf02b 3D \uf02b1) y \uf03d 0 \u0eaa\u0ebb\u0ea1\u0e9c\u0e99\u0ebb \u0e8a\u0ea7\u0ec8 \u0e8d\u0e84\u0eb7\u0ec8\u0eb5 r3 \uf02b 3r2 \uf02b 3r \uf02b1 \uf03d 0 (r \uf02b1)(r2 \uf02b 2r \uf02b1) \uf03d 0 (r \uf02b1)(r \uf02b1)(r \uf02b1) \uf03d 0 r \uf03d \uf02d1, \uf02d1, \uf02d1 \u0eaa\u0eb0\u0e99\u0e99\u0ec9\u0eb1 yc \uf03d c1e\uf02dx \uf02b c2xe\uf02dx \uf02b c3x2e\uf02dx \u0ec2\u0e94\u0e8d\u0e97\u0eb5\u0ec8 y1 \uf03d e\uf02dx ; y2 \uf03d xe\uf02dx \u0ec1\u0ea5\u0eb0 y3 \uf03d x2e\uf02dx \u0eaa\u0ebb\u0ea1\u0ea1\u0eb8\u0e94\u0e9c\u0e99\u0ebb \u0eaa\u0eb0\u0ec0\u0ea5\u0e8d\u0ec8 \u0eaa\u0eb0\u0ec0\u0e9e\u0eb3\u0eb0\u0e84\u0ec8\u0eb5\u0eb7: yp \uf03d v1e\uf02dx \uf02b v2xe\uf02dx \uf02b v3x2ex \u0e81\u0eb3\u0e99\u0e94\u0ebb \u0ec0\u0e87\u0ec8\u0ead\u0eb5\u0eb7 \u0e99\u0ec4\u0e82\u0ec0\u0e9e\u0eb7\u0eb5\u0ec8\u0ead\u0e88\u0eb0\u0eab\u0eb3\u0e84\u0ec8\u0eb3\u0e82\u0ead\u0e87 v1, v2, v3 \u0e88\u0eb3\u0e81\u0ea5\u0eb0\u0e9a\u0ebb\u0e9a\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99\u0e94\u0eb1\u0e87\u0ec8 \u0e99\u0eb5\u0eb1\u0ec9: \uf0ec \uf0ef\uf0ed\uf0ef\uf0efvv11\uf0a2\uf0a2 y1 \uf02b v2\uf0a2 y2 \uf02b v3\uf0a2 y3 \uf03d 0 y1\uf0a2 \uf02b v2\uf0a2 y2\uf0a2 \uf02b v3\uf0a2 y3\uf0a2 \uf03d 0 \uf0ef f (x) \uf0ef\uf0ee\uf0efv1\uf0a2y1\uf0a2\uf0a2\uf02b v2\uf0a2 y2\uf0a2\uf0a2 \uf02b v3\uf0a2 y3\uf0a2\uf0a2 \uf03d a0 \u0e88\u0eb3\u0e81 (D3 \uf02b 3D2 \uf02b 3D \uf02b1) y \uf03d ex \u0e88\u0eb0\u0ec4\u0e94\u0ec9 f (x) \uf03d ex ,a 0\uf03d1 3 3 \uf0ec \uf028 \uf029 \uf028 \uf029\uf0ef\uf0ef\uf0ef\uf0edv\uf02d1\uf0a2ve1\uf0a2\uf02dex\uf02d\uf02bx \uf02bv2\uf0a2vx2\uf0a2e\uf02dex\uf02d\uf02bx v3\uf0a2 x 2e\uf02d x \uf03d0 \uf02d xe\uf02dx \uf02b v3\uf0a2 \u0e88\u0eb0\u0ec4\u0e94\u0ea5\u0ec9 \u0eb0\u0e9a\u0ebb\u0e9a\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99 2xe\uf02dx 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\u0eaa\u0ebb\u0ea1\u0ea1\u0eb8\u0e94\u0ea7\u0eb3\u0ec8 \u0eaa\u0ea1\u0ebb \u0e9c\u0ebb\u0e99\u0ea1\u0eb5\u0ec3\u0e88\u0e9c\u0ebb\u0e99\u0ec1\u0ea1\u0e99\u0ec8 y0(x) \uf03d C1y1(x) \uf02b C2y2(x). \u0e9a\u0eb3\u0e94\u0e81\u0ec9\u0eb3\u0ea7\u0e97\u0eb5 2: \u0e8a\u0ead\u0e81\u0ec3\u0e88\u0e9c\u0e99\u0ebb \u0e97\u0ebb\u0ea7\u0ec8\u0eb1 \u0ec4\u0e9b y(x) \uf03d C1(x)y1(x) \uf02b C2(x)y2(x) \u0e94\u0ea7\u0ec9 \u0e8d\u0ea5\u0eb0\u0e9a\u0e9a\u0ebb \u0eaa\u0ebb\u0ea1\u0e9c\u0e99\u0ebb \uf0ec\uf0ed\uf0eeCC11'' (x ) y1 ( x) \uf02b C' (x ) y 2 ( x) \uf03d 0 x ) (x ) y1 ( x) \uf02b 2 (x ) y 2 ( x) \uf03d f( C' 2 \u0e9a\u0eb3\u0e94\u0e81\u0ec9\u0eb3\u0ea7\u0e97\u0eb5 3: \u0ec1\u0e97\u0e99\u0e84\u0ec8\u0eb3 C1(x), C2(x), y1(x), y2(x) \u0ec3\u0eaa\u0ec8 y(x) \uf03d C1(x)y1(x) \uf02b C2(x)y2(x) \u0e95\u0ebb\u0ea7\u0ea2\u0ec8\u0eb9\u0eb3\u0e87 1: \u0ec1\u0e81\u0ec9\u0ea5\u0eb0\u0e9a\u0e9a\u0ebb \u0eaa\u0ebb\u0ea1\u0e9c\u0e99\u0ebb \u0e88\u0eb8\u0e99\u0ea5\u0eb0\u0e84\u0eb0\u0e99\u0e94\u0eb4 y\\\" \uf02b 4y' \uf02b 4y \uf03d e2x ln x \u0ea7\u0e97\u0eb4 \u0eb5\u0ec1\u0e81:\u0ec9 \u0e9a\u0eb3\u0e94\u0e81\u0ec9\u0eb3\u0ea7\u0e97\u0eb5 1: \u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99\u0ec0\u0ead\u0e81\u0eb0\u0e9e\u0e99 y\\\" \uf02b 4y \uf02b 4y \uf03d 0 \u0ec1\u0e81\u0eaa\u0ec9 \u0ea1\u0ebb \u0e9c\u0e99\u0ebb \u0e9a\u0ead\u0e81\u0ea5\u0e81\u0eaa\u0eb0\u0e99\u0eb0 r2 \uf02b 4r \uf02b 4 \uf03d 0 \uf0de r1 \uf03d r2 \uf03d \uf02d2. \u0eaa\u0ebb\u0ea1\u0e9c\u0e99\u0ebb \u0ea1\u0eb5\u0ec3\u0e88\u0e9c\u0ebb\u0e99\u0ec1\u0ea1\u0ec8\u0e99 y0 (x) \uf03d C e\uf02d2x \uf02b C 2 xe \uf02d2 x 1 \u0ec0\u0eae\u0eb3\u0ebb \u0e81\u0eb3\u0e99\u0e94\u0ebb y1(x) \uf03d e\uf02d2x \u0ec1\u0ea5\u0eb0 y2 (x) \uf03d xe\uf02d2x \u0e9a\u0eb3\u0e94\u0e81\u0ec9\u0eb3\u0ea7\u0e97\u0eb5 2: \u0e8a\u0ead\u0e81\u0eab\u0eb3\u0ec3\u0e88\u0e9c\u0e99\u0ebb \u0e97\u0ec8\u0ea7\u0ebb\u0eb1 \u0ec4\u0e9b y(x) \uf03d C1(x)y1(x) \uf02b C2(x)y2(x) \u0e94\u0ec9\u0ea7\u0e8d\u0ea5\u0eb0\u0e9a\u0e9a\u0ebb \u0eaa\u0ea1\u0ebb \u0e9c\u0e99\u0ebb \uf0ec\uf0ee\uf0edCC11'' (x ) y1 ( x ) \uf02b C' (x ) y 2 ( x ) \uf03d 0 \uf0de \uf0ed\uf0ee\uf0ecC\uf02d21' (Cx1')(ex\uf02d)2ex \uf02b C' (x)xe\uf02d2x \uf03d 0 (x ) y1 ( x ) \uf02b 2 (x ) y 2 ( x ) \uf03d f (x 2 \uf02d C' ) \uf02b\uf02d2 x C ' (x)(e \uf02d2 x 2xe \uf02d2 x ) \uf03d e \uf02d2 x ln x 2 2 \uf0ee\uf0ed\uf0ecC\uf02d21' (Cx1')( \uf02b xC'2 (x) \uf03d 0 (1) (2) x ) \uf02b C' (x)(1 \uf02d 2x ) \uf03d ln x 2 \uf0ee\uf0ec\uf0ed2\uf02dC2C1' (1'x( ) \uf02b 2xC'2 (x) \uf03d 0 (1) (2) x ) \uf02b C' (x).(1 \uf02d 2x ) \uf03d ln x 2 \u0ec0\u0eae\u0ebb\u0eb3\u0ec0\u0ead\u0ebb\u0eb3 (1)+(2) : C' ( x ) \uf03d ln x 2 d\uf05bC2 (x)\uf05d \uf03d ln x dx 163","\uf0f2 d\uf05bC2(x)\uf05d \uf03d \uf0f2ln x dx C2(x) \uf03d x ln x \uf02d x \uf02b K2 \u0e88\u0eb3\u0e81 (1): C' (x ) \uf02b xC'2 (x) \uf03d 0 1 C' (x ) \uf03d xC'2 (x) 1 C' (x) \uf03d \uf02d x ln x 1 d\uf05bC1(x)\uf05d \uf03d \uf02dx ln x dx \uf0f2 d\uf05bC1(x)\uf05d \uf03d \uf02d\uf0f2 x ln x dx C1(x) \uf03d \uf02d x2 ln x \uf02b x2 \uf02b K1 2 4 \u0e9a\u0eb3\u0e94\u0e81\u0ec9\u0eb3\u0ea7\u0e97\u0eb5 3: \u0ec1\u0e97\u0e99\u0e84\u0ec8\u0eb3\u0e82\u0ead\u0e87 C1(x), C2(x), y1(x), y2(x) \u0ec3\u0eaa\u0ec8 y(x) \uf03d C1(x)y1(x) \uf02b C2(x)y2(x) , \u0ec0\u0eae\u0ebb\u0eb3\u0ec4\u0e94:\u0ec9 y(x) \uf03d \uf0e6 \uf02d x2 ln x \uf02b x2 \uf02b K1 \uf0f6 e \uf02d2 x \uf02b (x ln x \uf02d x \uf02b K2 )xe\uf02d2x \uf0e7\uf0e8 2 4 \uf0f7\uf0f8 \u0e95\u0ea7\u0ebb \u0ea2\u0eb9\u0ec8\u0eb3\u0e87 2: \u0ec1\u0e81\u0ea5\u0ec9 \u0eb0\u0e9a\u0ebb\u0e9a\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99\u0e88\u0eb8\u0e99\u0ea5\u0eb0\u0e84\u0eb0\u0e99\u0eb4\u0e94 y\\\" \uf02d 3y' \uf02b 2y \uf03d ex (x \uf02b1) \u0ea7\u0e97\u0eb4 \u0ec1\u0eb5 \u0e81\u0ec9: \u0e9a\u0eb3\u0e94\u0e81\u0ec9\u0eb3\u0ea7\u0e97\u0eb5 1: \u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99\u0ec0\u0ead\u0e81\u0eb0\u0e9e\u0e99 y\\\" \uf02d 3y' \uf02b 2y \uf03d 0 \u0ec1\u0e81\u0ec9\u0eaa\u0ea1\u0ebb \u0e9c\u0ebb\u0e99\u0e9a\u0ead\u0e81\u0ea5\u0e81\u0eaa\u0eb0\u0e99\u0eb0 r2 \uf02d 3r \uf02b 2 \uf03d 0 \uf0de r1 \uf03d 1, r2 \uf03d 2. \u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99\u0ea1\u0eb5\u0ec3\u0e88\u0e9c\u0ebb\u0e99\u0ec1\u0ea1\u0ec8\u0e99 y0 (x) \uf03d C1ex \uf02b C2e2x. \u0ec0\u0eae\u0eb3\u0ebb \u0e81\u0eb3\u0e99\u0ebb\u0e94 y1(x) \uf03d ex \u0ec1\u0ea5\u0eb0 y2 (x) \uf03d e2x \u0e9a\u0eb3\u0e94\u0e81\u0ec9\u0eb3\u0ea7\u0e97\u0eb5 2: \u0e8a\u0ead\u0e81\u0eab\u0eb3\u0ec3\u0e88\u0e9c\u0e99\u0ebb \u0e97\u0ec8\u0ea7\u0eb1\u0ebb \u0ec4\u0e9b y(x) \uf03d C1(x)y1(x) \uf02b C2(x)y2(x) \u0e94\u0ec9\u0ea7\u0e8d\u0ea5\u0eb0\u0e9a\u0ebb\u0e9a\u0eaa\u0ebb\u0ea1\u0e9c\u0e99\u0ebb \uf0ec\uf0ed\uf0eeCC11'' (x ) y1 ( x ) \uf02b C' (x ) y 2 (x) \uf03d 0 x ) : (x ) y1 ( x ) \uf02b 2 (x ) y 2 (x) \uf03d f( C' 2 \uf0ed\uf0ee\uf0ecCC11'' (x ).e x \uf02b C' ( x ).e 2 x \uf03d 0 (1) (x ).e x \uf02b 2 (2) 2e2x.C'2 (x) \uf03d ex (x \uf02b 1) \uf0ee\uf0ed\uf0ecCC11'' (x ) \uf02b C' (x).ex \uf03d0 \uf02b 1 (1) (x ) \uf02b 2 x.C'2 (x )\uf03dx (2) 2e \u0ec0\u0eae\u0eb3\u0ebb \u0ec0\u0ead\u0ebb\u0eb3 (1) - (2) : e x C' (x) \uf03d x \uf02b 1 2 164","C2 (x) \uf03d \uf0f2 (x \uf02b1)e\uf02dxdx C2 (x) \uf03d \uf02d(x \uf02b 1)e\uf02dx \uf02d e\uf02dx \uf02b K2 \u0e88\u0eb3\u0e81 (1): C' (x ) \uf02b C' ( x).e x \uf03d 0 1 2 C' (x ) \uf03d \uf02dC'2e \uf02d x 1 C' (x ) \uf03d \uf02d( x \uf02b 1) 1 C1(x) \uf03d \uf02d\uf0f2 (x \uf02b1)dx C1(x) \uf03d \uf02d 1 x2 \uf02d x \uf02b K1 2 \u0e9a\u0eb3\u0e94\u0e81\u0ec9\u0eb3\u0ea7\u0e97\u0eb5 3: \u0ec1\u0e97\u0e99\u0e84\u0ec8\u0eb3\u0e82\u0ead\u0e87 C1(x), C2(x), y1(x), y2(x) \u0ec3\u0eaa\u0ec8 y(x) \uf03d C1(x)y1(x) \uf02b C2(x)y2(x) , \u0ec0\u0eae\u0ebb\u0eb3\u0ec4\u0e94:\u0ec9 y(x) \uf03d \uf0e6 \uf02d 1 x2 \uf02d x \uf02b K1 \uf0f6 ex \uf02b (\uf02d(x \uf02b 1)e\uf02dx \uf02d e\uf02dx \uf02b K2 )e2x. \uf0e8\uf0e7 2 \uf0f7\uf0f8 \u0e95\u0ea7\u0ebb \u0ea2\u0ec8\u0eb9\u0eb3\u0e87 3: \u0ec1\u0e81\u0ec9\u0ea5\u0eb0\u0e9a\u0ebb\u0e9a\u0eaa\u0ebb\u0ea1\u0e9c\u0e99\u0ebb \u0e88\u0eb8\u0e99\u0ea5\u0eb0\u0e84\u0eb0\u0e99\u0eb4\u0e94 y\\\" \uf02b y \uf03d tan x \u0ea7\u0e97\u0eb4 \u0eb5\u0ec1\u0e81:\u0ec9 \u0e9a\u0eb3\u0e94\u0e81\u0ec9\u0eb3\u0ea7\u0e97\u0eb5 1: \u0eaa\u0ebb\u0ea1\u0e9c\u0e99\u0ebb \u0ec0\u0ead\u0e81\u0eb0\u0e9e\u0e99 y\\\" \uf02b y \uf03d 0 \u0ec1\u0e81\u0eaa\u0ec9 \u0ea1\u0ebb \u0e9c\u0ebb\u0e99\u0e9a\u0ead\u0e81\u0ea5\u0e81\u0eaa\u0eb0\u0e99\u0eb0 r2 \uf02b1 \uf03d 0 \uf0de r \uf03d \uf0b1i \u0eaa\u0ea1\u0ebb \u0e9c\u0ebb\u0e99\u0ea1\u0eb5\u0ec3\u0e88\u0e9c\u0e99\u0ebb \u0ec1\u0ea1\u0ec8\u0e99 y0(x) \uf03d C1 cos x \uf02b C2 sin x \u0eaa\u0eb0\u0ec1\u0e94\u0e87\u0ea7\u0ec8\u0eb3 y1(x) \uf03d cos x \u0ec1\u0ea5\u0eb0 y2(x) \uf03d sin x \u0e9a\u0eb3\u0e94\u0e81\u0ec9\u0eb3\u0ea7\u0e97\u0eb5 2: \u0e8a\u0ead\u0e81\u0eab\u0eb3\u0ec3\u0e88\u0e9c\u0ebb\u0e99\u0e97\u0ec8\u0ea7\u0eb1\u0ebb \u0ec4\u0e9b y(x) \uf03d C1(x)y1(x) \uf02b C2(x)y2(x) \u0e94\u0ec9\u0ea7\u0e8d\u0ea5\u0eb0\u0e9a\u0e9a\u0ebb \u0eaa\u0ea1\u0ebb \u0e9c\u0e99\u0ebb \uf0ed\uf0ec\uf0eeCC11'' (x ) y1 ( x ) \uf02b C' (x ) y 2 (x) \uf03d 0 x ) : (x ) y1 ( x ) \uf02b 2 (x ) y 2 (x) \uf03d f( C' 2 \uf0ed\uf0ee\uf0ecC\uf02dC1' (1'x()xc)ossinxx\uf02b\uf02bCC'2 ('2x(x)s)icnoxs \uf03d0 tan x (1) x\uf03d (2) \uf0ed\uf0ec\uf0eeC\uf02dC1' (1'x()x.)s.icnoxs cos x \uf02b C' ( x ).sin 2 x \uf03d0 (1) x sin 2 x \uf03d sin (2) x \uf02b C' ( x ) cos 2 x 2 \u0ec0\u0eae\u0eb3\u0ebb \u0ec0\u0ead\u0ebb\u0eb3 (1) + (2) : C' (x ) \uf03d sin x 2 C2(x) \uf03d \uf0f2sin xdx C2(x) \uf03d \uf02dcos x \uf02b K2 \u0e88\u0eb3\u0e81 (1): C' (x ) cos x \uf02b C' ( x ) sin x \uf03d 0 1 2 165","C1' ( x) \uf03d \uf02d C'2 sin x cos x C' (x ) \uf03d \uf02dC2 (x ) tan x 1 C' (x ) \uf03d \uf02d sin x tan x 1 C1 (x ) \uf03d \uf02d \uf0f2 sin2 x dx cos x C1 (x ) \uf03d \uf02d \uf0f2 sin2 x d(sin x) cos x C1 (x ) \uf03d \uf02d \uf0f2 1 sin2 x x d(sin x) \uf02d sin2 C1 (x ) \uf03d \uf0f2 sin2 x 1 d(sin x ) sin2 x \uf02d C1 (x ) \uf03d \uf0f2 sin2 x \uf02d 1 \uf02b 1 d(sin x) sin2 x \uf02d 1 C1 (x ) \uf03d \uf0f2 \uf0e8\uf0e7\uf0e61 \uf02b sin 1 \uf02d 1 \uf0f6 d(sin x) 2x \uf0f8\uf0f7 C1(x) \uf03d \uf0f2 \uf0e7\uf0e61 \uf02b (sin x \uf02d 1 x \uf02b 1) \uf0f6 d(sin x) \uf0e8 1) (sin \uf0f7 \uf0f8 C1 (x) \uf03d \uf0f2 d(sin x ) \uf02b \uf0f2 (sin x \uf02d 1 x \uf02b 1) d(sin x) 1) (sin C1(x) \uf03d sin x \uf02b 1 \uf0f2 (sin x 2 x \uf02b 1) d(sin x) 2 \uf02d 1) (sin C1(x) \uf03d sin x \uf02b 1 \uf0f2 \uf0e6 sin 1 \uf02d 1 \uf02d sin 1 \uf02b 1 \uf0f6 d(sin x) 2 \uf0e7\uf0e8 x x \uf0f7\uf0f8 C1 (x ) \uf03d sin x \uf02b 1 \uf0f2 d(sin x) \uf02d 1 \uf0f2 d(sin x) 2 sin x \uf02d1 2 sin x \uf02b1 C1(x) \uf03d sin x \uf02b 1 ln sin x \uf02d1 \uf02d 1 sin x \uf02b1 \uf02b K1 2 2 166","C1(x) \uf03d sin x \uf02b 1 ln sin x \uf02d1 \uf02b K1 2 1\uf02b sin x \u0e9a\u0eb3\u0e94\u0e81\u0ec9\u0eb3\u0ea7\u0e97\u0eb5 3: \u0ec1\u0e97\u0e99\u0e84\u0eb3\u0ec8 \u0e82\u0ead\u0e87 C1(x),C2 (x), y1(x), y2(x) \u0ec3\u0eaa\u0ec8 y(x)=C1(x)y1(x)+C2(x) y2(x): y(x)= \uf0e6 sinx+ 1 ln sinx-1 +K1 \uf0f6 cosx+ \uf028 -cosx+K 2 \uf029 sinx. \uf0e8\uf0e7 2 1+sinx \uf0f7\uf0f8 \u0e81\u0eb4\u0e94\u0e88\u0eb0\u0e81\u0eb3: \u0ec3\u0eab\u0ec9\u0e99\u0e81\u0eae\u0ebd\u0e99\u0ec1\u0e81\u0eaa\u0ec9 \u0ebb\u0ea1\u0e9c\u0e99\u0ebb \u0e88\u0eb8\u0e99\u0ea5\u0eb0\u0e84\u0eb0\u0e99\u0eb4\u0e94\u0ea5\u0eb5\u0ec0\u0e99\u0ec1\u0ead\u0ea5\u0ec8\u0eb8\u0ea1\u0e99\u0eb5\u0eb1\u0ec9\u0e94\u0ea7\u0ec9 \u0e8d\u0ea7\u0e97\u0eb4 \u0eb5 Lagrange 1. y\\\" +5y' +6y = 1 1+e2x 2. y\\\" + 2y' + y = 3e-x. 1+x \u0ea7\u0eb4\u0e97\u0eb5\u0ec1\u0e81\u0ec9 1. y\\\" +5y' +6y = 1 1+e2x +) \u0ec1\u0e81\u0ec9\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99\u0e9a\u0ead\u0e81\u0ea5\u0e81\u0eaa\u0eb0\u0e99\u0eb0: k2 +5k +6 = 0 \uf0db \uf0eck = -2 \uf0ed\uf0eek = -3 \uf0de yc = C e-2x + C e-3x 1 2 + \u0e8a\u0ead\u0e81 yP \u0e88\u0eb3\u0e81\u0eae\u0e9a\u0eb9 \u0eae\u0eb3\u0ec8 \u0e87: yP = C1.e-2x + C2 (x).e-3x \u0eaa\u0eb3\u0ea5\u0e9a C1(x), C2(x) \u0e95\u0ead\u0e9a\u0eaa\u0eb0\u0edd\u0ead\u0e87: 2 \uf0ec\uf0efC1' (x)e-2x +C'2 (x)e-3x =0 \uf0ee\uf0ef\uf0ed-2C1' 1 (x)e-2x +C'2 (x)e-3x = 1+e2x \uf0db \uf0ec\uf0ef\uf0ed-C'2 (x)e-3x = 1 1+e2x \uf0ef\uf0eeC1' (x)e-2x +C'2 (x)e-3x =0 \uf0ec\uf0ef\uf0efC'2 (x)e-3x = - e3x e2x +1 \uf0db \uf0ed \uf0ef\uf0ef\uf0eeC1' e 2x (x)= e2x +1 167","+) C1 (x) = \uf0f2 e2x = 1 \uf0f2 2e2x e2x +1 2 dx e2x +1 \uf028 \uf029C1(x) 1 1 = 2 ln e2x +1 = 2 ln e2x +1 +) C2 (x) = -\uf0f2 e3x dx e2x +1 \u0ea7\u0eb3\u0e87 t=ex \uf0dedt = exdx \uf0de C2 (x) = -\uf0f2 t 2dt = - \uf0f2 \uf0e6\uf0e7\uf0e81- t 1 \uf0f7\uf0f8\uf0f6dt t+1 2 +1 =-\uf028t -arctant\uf029 = arctanex -ex \uf028 \uf029 \uf028 \uf029\uf0de 1 yP = 2 e-2xln 1+e2x + e-3x arctanex -ex \u0ec3\u0e88\u0e9c\u0ebb\u0e99\u0ea5\u0ea7\u0ea1\u0e82\u0ead\u0e87\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99\u0ec1\u0ea1\u0e99\u0ec8 : \uf028 \uf029 \uf028 \uf029y 1 = C e-2x +C2e-3x + 2 e-2x ln 1+e2x + e-3x arctanex -ex 1 2. y\\\" + 2y' + y = 3e-x. 1+x +) \u0ec1\u0e81\u0eaa\u0ec9 \u0ea1\u0ebb \u0e9c\u0e99\u0ebb \u0e9a\u0ead\u0e81\u0ea5\u0e81\u0eaa\u0eb0\u0e99\u0eb0: k2 + 2k +1= 0 \uf0db k = -1 (\u0ec3\u0e88\u0e9c\u0ebb\u0e99\u0e84\u0ec8\u0eb9) \uf0de yc = e-x \uf028C1+C2x\uf029 yc = C1e-x + C2xe-x + \u0e8a\u0ead\u0e81 yP \u0e88\u0eb3\u0e81\u0eae\u0e9a\u0eb9 \u0eae\u0eb3\u0ec8 \u0e87: yP = C1(x)e-x + C2 (x)xe-x \u0eaa\u0eb3\u0ea5\u0e9a C1(x), C2(x) \u0e95\u0ead\u0e9a\u0eaa\u0eb0\u0edd\u0ead\u0e87: \uf0ec\uf0efC1' (x)e-x +C'2 (x)xe-x =0 \uf0ed \uf0ef\uf0ee-C1' (x)e-x +C'2 (x)(e-x -xe-x )=3e-x 1+x \uf0db \uf0ed\uf0ef\uf0ecC'2 (x)e-x = 3e-x 1+x \uf0ef\uf0eeC1' (x)e-x +C'2 (x)xe-x =0 \uf0db \uf0ef\uf0ed\uf0ecC'2 (x)e-3x =3 1+x \uf0ef\uf0eeC1' (x)= -3x 1+x 168","+) C1(x)=-3\uf0f2 x 1+xdx \u0ea7\u0eb3\u0e87 t= 1+x \uf0de t2 =1+x \uf0de dx = 2t dt \uf0de C1(x) =-3\uf0f2 (t2-1)t.2t dt =-6\uf0f2\uf028t4-t2 \uf029dt \uf0e6 t5 t3 \uf0f6 = -6\uf0e8\uf0e7 5 - 3 \uf0f8\uf0f7 C1 (x) = \uf02d 6 (1 \uf02b x)2 1 \uf02b x \uf02b 2(1\uf02b x) 1\uf02b x 5 1 +) C2 (x) =3\uf0f2 1+xdx=3\uf0f2 (1+x)2d(1+x) 23 = 3. (1+x)2 =2(1+x) 1+x 3 \uf0de C2 (x) = 2(1+x) 1+x \uf0de y P = e-x \uf0eb\uf0e9\uf0ea\uf02d 6 (1 \uf02b x)2 1\uf02b x \uf02b 2(1\uf02b x) 1\uf02b x \uf02b 2x(1\uf02b x) 1 \uf02b x \uf0f9 5 \uf0fa\uf0fb yP = e-x \uf0ea\uf0e9\uf0eb\uf02d 6 (1 \uf02b x)2 1\uf02b x \uf02b 2(1\uf02b x)2 1 \uf02b x \uf0f9 5 \uf0fa\uf0fb yP = 4 e-x (1 \uf02b x)2 1\uf02b x 5 \u0e94\u0eb1\u0e87\u0ec8 \u0e99\u0ec9\u0eb1\u0e99 \u0ec3\u0e88\u0e9c\u0e99\u0ebb \u0ea5\u0ea7\u0ea1\u0e82\u0ead\u0e87\u0eaa\u0ebb\u0ea1\u0e9c\u0e99\u0ebb \u0ec1\u0ea1\u0ec8\u0e99: y = e-x \uf0ea\uf0eb\uf0e9C1 +C2x+ 4 (1+x)5 \uf0f9 5 \uf0fb\uf0fa 169","\u0e9a\u0e94\u0ebb \u0ec0\u0e9d\u0eb4\u0e81\u0eab\u0e94 \u0e99\u0eb3\u0ec3\u0e8a\u0ec9 Lagrange \u0ec1\u0e81\u0eaa\u0ec9 \u0ebb\u0ea1\u0e9c\u0ebb\u0e99\u0e88\u0e99\u0eb8 \u0ea5\u0eb0\u0e84\u0eb0\u0e99\u0eb4\u0e94\u0ea5\u0ec0\u0eb5 \u0e99\u0ec1\u0ead\u0e82\u0e99\u0eb1\u0ec9 \u0eaa\u0ead\u0e87\u0ea5\u0ec8\u0eb8\u0ea1\u0e99:\u0eb5\u0eb1\u0ec9 1) y\\\" + y = xcosx 2) y\\\" + y = 4xsinx 3) y\\\" + y' + y = -13sinx 4) y\\\" + y = sinx 5) y\\\" + 4y = cos2x 6) y\\\" + y = cosx 7) y\\\" +9y =sin3x 8) y\\\" + 4y' + 4y = 1 e2xcos2x 2 9) y\\\" + y' -2y = excosx 10) y\\\" + y' -2y = -7exsinx \uf028 \uf02911) y\\\" + 2y' \uf02b 5y = e2x x2 +1 12) y\\\" +5y' \uf02b 6y =e2x \uf0282x +1\uf029 13) y\\\" + 4y' \uf02b 4y = e2x 14) y\\\" +5y =sin3x 15) y\\\" +3y' + 2y = x2 16) y\\\" - 4y' +5y = e-x 17) y\\\" - y' = xe2 y'(0)=1, y(0)=2 18) y\\\" - 3y' + 2y = (-12x + 4)ex 19) y\\\" + y = (x+2)cosx 20) y\\\" - 3y = excosx y(0)=1=y'(\u03c0) 21) y\\\" +9y = x2sinx 22) y\\\" +3y' - 4y = (x3 + x +1)ex 23) y\\\" + 2y' + 10y = x e2 -xcos3x 24) y\\\" + 2y' + 2y = xexsinx 25) y\\\" + y = xsinx 170","26) y\\\" + 4y = x 27) y\\\" - 2y' + y = e2x 28) y\\\" + y' = xe-x 29) y\\\" - 3y' + 2y = xe3x 30) y\\\" - 4y' +8y =sin2x 31) y\\\" + 2y' + y = xcosx 32) y\\\" - y' - 6y =1+ e-2x 33) 9y\\\" + y = 3x +e-x y(0) =1, y'(0) = 2 34) y\\\" +9y = 6cos3x 35) y\\\" + y = 3sinx 36) y\\\" + y' = ex + 2cosx 37) 9y\\\" + y = -2sinx y'(0) =1, y \uf0e7\uf0e6\uf0e8 \uf070 \uf0f7\uf0f6\uf0f8 =1 \u03c0 2 38) y\\\" + y =secx 39) y\\\" +9y = x2sinx 0<x< 2 40) y\\\" + 2y' +10 y = x e2 -xcos3x 41) y\\\" -2y' + 2 y = xexsinx 42) y\\\" + y = 2cosx 43) y\\\" + y = xsinx 44) y\\\" + 4y = x 45) y\\\" - 2y' + y = e2x 46) y\\\" -5y' +6 y = (x+1)e2x 47) y\\\" - y' = xe-x 48) y\\\" -3y' + 2y = xe3x 49) y\\\" -4y' + 8y =sin 2x 50) y\\\" -2y' + y = xcosx 51) y\\\" - y' - 6y =1+ e-2x 171","52) 9y\\\" + y' =3x +e-x y(0)=1, y'(0)=2 53) y\\\" +9y = 6cos3x 54) y\\\" + y = 3sinx 55) y\\\" + y' = ex + 2cosx 56) y\\\" + y = -2sinx y'(0)=1, y \uf0e6\uf0e8\uf0e7 \u03c0 \uf0f6\uf0f7\uf0f8 =1 2 57) y\\\" -3y' 1 + 2y = 1+ e-x 58) y\\\" - y = 1 x 59) y\\\" - 4y' +5y = e2x cosx 60) y\\\" -2y' + y = ex 1+ x2 61) y\\\" - y' 1 = 1+ ex 62) y\\\" + y' -2y =1- x 63) y\\\" -4y' +3y = ex (x+2) 64) y\\\" -2y + y = x.ex 65) y\\\" -3y' +2y = 2sinx 66) y\\\" + y = x.cosx \uf076 \u0ec0\u0e97\u0e81\u0e99\u0e81\u0eb4 \u0e81\u0eb3\u0e99\u0ec1\u0e81\u0e81\u0ec9 \u0eb3\u0e99\u0ec1\u0e81\u0e9a\u0ec9 \u0e94\u0ebb \u0ec0\u0ea5\u0e81\u0eaa\u0ea1\u0ebb \u0e9c\u0e99\u0ebb \u0e88\u0e99\u0eb8 \u0ea5\u0eb0\u0e84\u0eb0\u0e99\u0e94\u0eb4 \u0ec1\u0e9a\u0e9a\u0e95\u0eb3\u0ec8 \u0e87\u0ec6 \uf09f \u0eae\u0eb9\u0e9a\u0eae\u0eb3\u0ec8 \u0e87 y ' \uf03d f (x) \u0eab\u0eb7 dy \uf03d f (x) dx \u0ec1\u0e99\u0eb0\u0e99\u0eb3\u0ea7\u0e97\u0eb4 \u0eb5\u0eab\u0eb3\u0ec3\u0e88\u0e9c\u0ebb\u0e99\u0ec0\u0eae\u0ebb\u0eb3\u0ea1\u0eb5 y' \uf03d f (x) dy \uf03d f (x) dx dy \uf03d f (x)dx \uf0f2 dy \uf03d \uf0f2 f (x)dx y \uf03d \uf0f2 f (x)dx \uf02b C \uf0de y \uf03d F(x) \uf02b C \u0ec0\u0ea1\u0eb5\u0ec8\u0ead\u0eb7 F(x) \u0ec0\u0e9b\u0e99\u0eb1 \u0ec0\u0e84\u0eb3\u0ec9\u0ebb\u0eb1 \u0e95\u0eb3\u0ea5\u0eb3\u0e82\u0ead\u0e87 f (x) \u0ec1\u0ea5\u0eb0 C \u0e84\u0ebb\u0e87\u0e84\u0eb3\u0ec8 . 172","\u0e95\u0ea7\u0ebb \u0ea2\u0eb3\u0ec8\u0eb9 \u0e87. y' \uf03d 2x \uf02b1 \u0ea7\u0e97\u0eb4 \u0ec1\u0eb5 \u0e81\u0ec9: \u0e88\u0eb3\u0e81 y' \uf03d 2x \uf02b1 dy \uf03d 2x \uf02b1 dx dy \uf03d (2x \uf02b1)dx \uf0f2 dy \uf03d \uf0f2 f (x)dx y \uf03d x2 \uf02b x \uf02b C \u0e94\u0ec8\u0e87\u0eb1 \u0e99\u0ec9\u0eb1\u0e99 \u0ec3\u0e88\u0e9c\u0e99\u0ebb \u0e97\u0eb5\u0ec0\u0ec8 \u0eae\u0ebb\u0eb3\u0e95\u0ec9\u0ead\u0e87\u0e81\u0eb3\u0e99\u0e8a\u0ead\u0e81\u0ec1\u0ea1\u0ec8\u0e99 y \uf03d x2 \uf02b x \uf02b C \uf09f \u0eae\u0eb9\u0e9a\u0eae\u0eb3\u0ec8 \u0e87 y' \uf03d ax2 1 \uf02b bx \uf02b c \uf09f \u0ec1\u0e99\u0eb0\u0e99\u0eb3\u0ea7\u0eb4\u0e97\u0ec1\u0eb5 \u0e81\u0ec9 \u0ec0\u0eae\u0ebb\u0eb3\u0ea1\u0eb5 y ' \uf03d ax2 1 \uf02b c \uf02b bx dy \uf03d 1 dx ax2 \uf02b bx \uf02b c dy \uf03d ax2 1 \uf02b c dx \uf02b bx \uf0f2 dy \uf03d \uf0f2 ax2 1 \uf02b c dx \uf02b bx y \uf03d \uf0f2 ax2 1 \uf02b c dx \uf02b bx \uf09f \u0e96\u0ec9\u0eb3\u0ea7\u0ec8\u0eb3 \uf044\uf03e0 \u0ec1\u0ea1\u0ec8\u0e99: y \uf03d 1 ln x \uf02d x1 \uf02b C. a(x1 \uf02d x2 ) x \uf02d x2 \uf09f \u0e96\u0eb3\u0ec9 \u0ea7\u0ec8\u0eb3 \uf044\uf03d0 \u0ec1\u0ea1\u0ec8\u0e99: y \uf03d \uf02d1 \uf02b C. a(x \uf02d x0) \uf09f \u0e96\u0eb3\u0ec9 \u0ea7\u0ec8\u0eb3 \uf044 \uf03c 0 \u0ec1\u0ea1\u0ec8\u0e99: y \uf03d 1 x\uf02bb\uf02d \uf02db2 \uf02b 4ac 2a ln 2 4a2 \uf02b C \uf02db2 \uf02b 4ac 4a 2 x\uf02bb\uf02b \uf02db2 \uf02b 4ac 2 4a 2 \u0e95\u0ea7\u0ebb \u0ea2\u0eb3\u0eb9\u0ec8 \u0e87 \u0ec1\u0e81\u0ec9\u0eaa\u0ebb\u0ea1\u0e9c\u0ebb\u0e99 y'\uf03d 1 x2 \uf02d 3x \uf02b 2 \u0ea7\u0eb4\u0e97\u0ec1\u0eb5 \u0e81:\u0ec9 \u0ec0\u0eae\u0eb3\u0ebb \u0ea1\u0eb5 y ' \uf03d x2 1 \uf02b 2 \uf02d 3x dy \uf03d 1 dx x2 \uf02d 3x \uf02b 2 173","dy \uf03d x2 \uf02d 1 \uf02b 2 dx 3x \uf0f2 dy \uf03d \uf0f2 x2 \uf02d 1 \uf02b dx 3x 2 y \uf03d \uf0f2 x2 \uf02d 1 \uf02b dx 3x 2 y \uf03d \uf0f2 (x \uf02d dx \uf02d1) 2)(x y \uf03d \uf0f2 \uf0e6 (x 1 2) \uf02d (x 1 \uf0f6 \uf0e7 \uf02d \uf02d1) \uf0f7dx \uf0e8 \uf0f8 y \uf03d \uf0f2 x 1 2 dx \uf02d \uf0f2 x 1 dx \uf02d \uf02d1 y \uf03d \uf0f2 x 1 2 d(x \uf02d 2) \uf02d \uf0f2 1 d(x \uf02d1) \uf02d x \uf02d1 y \uf03d ln x \uf02d 2 \uf02d ln x \uf02d1 \uf02b C y \uf03d ln x \uf02d 2 \uf02b C x \uf02d1 \u0e94\u0ec8\u0eb1\u0e87\u0e99\u0e99\u0eb1\u0ec9 \u0ec3\u0e88\u0e9c\u0e99\u0ebb \u0e82\u0ead\u0e87\u0eaa\u0ea1\u0ebb \u0e9c\u0ebb\u0e99\u0ec1\u0ea1\u0e99\u0ec8 y \uf03d ln x\uf02d2 \uf02bC x \uf02d1 \uf09f \u0eae\u0eb9\u0e9a\u0eae\u0eb3\u0ec8 \u0e87 y' \uf03d mx \uf02b n ax2 \uf02b bx \uf02b c \uf09f \u0ec1\u0e99\u0eb0\u0e99\u0eb3\u0ea7\u0eb4\u0e97\u0ec1\u0eb5 \u0e81\u0ec9 \u0ec0\u0eae\u0ebb\u0eb3\u0ea1\u0eb5 y ' \uf03d mx \uf02b n c ax2 \uf02b bx \uf02b dy \uf03d mx \uf02b n dx ax2 \uf02b bx \uf02b c dy \uf03d mx \uf02b n c dx ax2 \uf02b bx \uf02b \uf0f2 dy \uf03d \uf0f2 mx \uf02bn c dx ax2 \uf02b bx \uf02b \uf0f2y \uf03d \uf0e6 ax 2 mx \uf02b c \uf02b ax 2 n \uf02b c \uf0f6 dx \uf0e7\uf0e8 \uf02b bx \uf02b bx \uf0f7\uf0f8 y \uf03d \uf0f2 ax2 mx \uf02b c dx \uf02b \uf0f2 ax2 n \uf02b c dx \uf02b bx \uf02b bx y \uf03d m\uf0f2 ax2 x \uf02b c dx \uf02b n\uf0f2 ax2 1 \uf02b c dx \uf02b bx \uf02b bx y \uf03d m \uf0f2 ax2 2ax \uf02b c dx \uf02b n\uf0f2 ax2 1 \uf02b c dx 2a \uf02b bx \uf02b bx 174","y \uf03d m \uf0f2 2ax \uf02b b \uf02d b dx \uf02b n\uf0f2 ax2 1 \uf02b c dx 2a ax2 \uf02b bx \uf02b c \uf02b bx 2ax \uf02b b ax2 \uf02b bx \uf02b \uf0f2 \uf0f2y \uf03d m \uf0e6 \uf02d b \uf0f6 dx \uf02b n 1 2a \uf0e7\uf0e8 \uf02b bx \uf0f7\uf0f8 ax2 \uf02b bx \uf02b c dx c ax 2 \uf02b c y \uf03d m \uf0f2 2ax \uf02b b c dx \uf02d m \uf0f2 ax2 b \uf02b c dx \uf02b n\uf0f2 ax 2 1 \uf02b c dx 2a ax2 \uf02b bx \uf02b 2a \uf02b bx \uf02b bx d(ax2 \uf02b bx \uf02b c) \uf02d mb 1 1 ax2 \uf02b bx \uf02b c 2a \uf02b bx ax2 \uf02b bx \uf02b c dx \uf0f2 \uf0f2 \uf0f2y \uf03d m dx \uf02b n 2a ax2 \uf02b c m ax 2 \uf0e6 mb \uf0f6 1 \uf0f2y \uf03d 2a ln \uf02b bx \uf02b c \uf02b \uf0e7\uf0e8 \uf02d 2a \uf02b n \uf0f7\uf0f8 dx \uf0e6 b c \uf0f6 a \uf0e8\uf0e7 x2 \uf02b a x \uf02b a \uf0f7\uf0f8 m ax 2 1 \uf0e6 mb \uf0f6 1 dx \uf0f2y \uf03d 2a ln \uf02b bx \uf02b c \uf02b a \uf0e7\uf0e8 \uf02d 2a \uf02b n \uf0f7\uf0f8 \uf0e6 b c \uf0f6 \uf0e7\uf0e8 a a \uf0f7\uf0f8 x 2 \uf02b x \uf02b m ax2 1 \uf0e6 mb \uf0f6 1 dx \uf0f2y \uf03d 2a ln \uf02b bx \uf02b c \uf02b a \uf0e7\uf0e8 \uf02d 2a \uf02b n \uf0f8\uf0f7 x2 \uf02b b x \uf02b c aa \u0e99\u0eb3\u0ec3\u0e8a\u0ec9\u0eaa\u0eb9\u0e94: x2 \uf02b bx \uf03d \uf0e6 x \uf02b b \uf0f62 \uf02d b2 \uf0e7\uf0e8 a \uf0f7\uf0f8 a2 y \uf03d m ln ax 2 \uf02b bx \uf02b c \uf02b 1 \uf0e6 \uf02d mb \uf02b n \uf0f6 \uf0f2 1 dx 2a a \uf0e7\uf0e8 2a \uf0f8\uf0f7 b \uf0f62 \uf0e6 b \uf0f62 \uf0e6 \uf0e7 \uf0f7 \uf0e7 \uf0f7 \uf0e7x \uf02b a \uf0f7 \uf02d\uf0e7 a \uf0f7 \uf02bc \uf0e7 2 \uf0f7 2 \uf0f7 a \uf0e7 \uf0e8 \uf0f8 \uf0e8\uf0f8 m ax 2 1 \uf0e6 mb \uf0f6 1 \uf0f2y \uf03d 2a ln \uf02b bx \uf02b c \uf02b a \uf0e7\uf0e8 \uf02d 2a \uf02b n \uf0f7\uf0f8 \uf0f62 \uf02d \uf0f62 dx \uf0f7\uf0f8 \uf0f8\uf0f7 \uf0e6 x \uf02b b \uf0e6 b \uf02b c \uf0e8\uf0e7 2a \uf0e8\uf0e7 2a a m ax 2 1 \uf0e6 mb \uf0f6 1 \uf0f2y \uf03d 2a ln \uf02b bx \uf02b c 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