plzzzz need help ODEs

$(\cos x) (e^y -y) \frac{dy}{dx}=e^y\sin 2x $
i did these steps but i couldnt continue

separate variables
$\Large (1 - ye^{-y})dy = \frac{2\sin(x)\cos(x)}{\cos(x)}dx$
@ganeshie8 @terenzreignz

Question

plzzzz need help ODEs  

$(\cos x) (e^y -y) \frac{dy}{dx}=e^y\sin 2x $
i did these  steps but i couldnt continue

separate variables
$\Large (1 - ye^{-y})dy = \frac{2\sin(x)\cos(x)}{\cos(x)}dx$
@ganeshie8 @terenzreignz

usukidoll · Answer

errr you could just cancel out the cosx and then take the antiderivative on both sides to see what you have

anonymous · Answer

Why not just integrate?

anonymous · Answer

$$
\int 2\sin(x)\;dx = -2\cos(x)+C
$$

usukidoll · Answer

oh sorry yeah .. integrate... XD

usukidoll · Answer

yeah that's right integrate both sides... 

integration by parts for y?!

ikram002p · Answer

@BSwan check it out !

anonymous · Answer

by exact ??

usukidoll · Answer

exact? for real? that has to be in the form of M (x,y) dy + N (x,y) dx = 0

usukidoll · Answer

then you have to take My and Nx and if they are not the same, you need to find the integrating factor... still won't work? then exact isn't a good choice

anonymous · Answer

sin2x=2sinxcosx, so
$(e^y-y)dy/dx=2\sin x e^y$
separating variables:
$1-ye^{-y}dy=2sinxdx$

ankitshaw · Answer

$$(1-y/e^y)dy = 2sinxdx  $$
now u can use substitution method in LHS to solve it..
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