I'm working on this problem which I don't know how to approach.
I need to find a general solution of a given ODE, and here is the equation:
$(2x\sin(y)\cos(y))y' = 4x^2 + \sin^2y$
I feel like substituting $2y$ as $v$ should be the right way to solve it, but it didn't work out very well for me - the trigonometry got super weird.
Substituting $\sin(y)$ as $v$ didn't work out very well either. So I'm kinda out of options.
Any suggestions?
$$(2x\sin(y)\cos(y))y' = 4x^2 + \sin^2y$$ $u= \sin^2y$
$u'=2\sin(y)\cos(y)y'$ $$xu' =4x^2 + u$$ Linear ODE easy to solve : $$u=4x^2+cx$$ $$y=\pm\arcsin\left(\sqrt{4x^2+cx}\right)$$