Originally Posted by

**valerie-petit** Hi everyone,

If anyone could help to check if no mistake in my calculation.

Here is the question and my answer:

Hence find, an implicit form, the general solution of the differential equation

dy/dx = __2y__3/2__ cos x__

(2 + sin x)2

The differential equation dy/dx = 2y3/2 cos x/(2+sin x)2,

Has a right-hand side of the form f(x) g(y), where

g(y) = 2y 3/2 cos x and f(x) = (2+sin x)2

Dividing both sides of the differential equation by g(y) means multiplying both sides by y. This give

∫ 2y 3/2 cos x dy = ∫(2+sin x)2 dx

y5/2-sin x + a = cos x3 + b

Thus the general solution, in implicit form, is

y 5/2 = cos x3 + c

Thanks for your help