2(∫_0 ^( x) y^3 cos xdx)[((yd^2 y)/dx^2 )−((dy/dx))^2 ] = ky^5 sin x ; y(0)=a, y′(0)=0 . solve the differential equation. (Laplace tranforms might be helpful, i think).


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Question Number 61635 by ajfour last updated on 05/Jun/19

$2 (\int_{0}^{x} y^{3} \cos x d x) [\frac{{y d}^{2} y}{{d x}^{2}} - {(\frac{d y}{d x})}^{2}]$ $= {k y}^{5} \sin x;$ $y (0) = a, y^{'} (0) = 0 .$ $s o l v e t h e d i f f e r e n t i a l e q u a t i o n .$ $(L a p l a c e t r a n f o r m s m i g h t$ $b e h e l p f u l, i t h i n k) .$
	Answered by perlman last updated on 05/Jun/19

	$y e a h \int y^{3} c o s (x) \neq y^{3} s i n (x) ==$ $i w i l l t r y [i t [$
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