solve the equation:

$\displaystyle (3\sin{y} - 5x)dx +2x^2\cot{y}dy=0$

this is a tough problem for me that i cant start...

i can't find any separable nor any linearity in this solution

ill try to solve

solution:

$\displaystyle (3\sin{y} - 5x)dx +2x^2\frac{\cos{y}}{\sin{y}}dy=0$

substitute let w = sin(y)

dw = cos(y)dy so substitute

$\displaystyle (3w - 5x)dx + 2x^2\frac{dw}{w} = 0$

$\displaystyle \frac{3w - 5x}{2x^2}dx = \frac{dw}{w} $

$\displaystyle 2x^2dw - 5xwdx = -3w^2dx$

$\displaystyle \frac{dw}{dx} - \frac{5w}{2x} = \frac{-3w^2}{2x^2}$

....

now im stuck