Solve THIS ODE $ (2x-y\sin(2x))dx = (\sin^2x-2y)dy $ The following problem is in Mathematical Methods in physical science CH8 miscellaneous problems
$$
(2x-y\sin(2x))dx = (\sin^2x-2y)dy
$$
it isnt an exact equation the only difference is $-$ sign
because it not an exact equation I tried to rearrange it to produce linear first order but it did not work
I dont know what to do
I assume there an integration factor for such problem to make it exact or methods
Also I tried to use Mathematica DSolve function to find a solution
DSolve[{y'[x] == (2 x - y[x] sin (2 x))/(sin^2 x - 2 y[x])}, y[x], x]

This what it produced
DSolve::deqn: Equation or list of equations expected instead of True in the first argument {True}.
DSolve[{True}, y[x], x]

thank you

Recall we say a differential equation of type
$$N(x,y)dx+M(x,y)dy=0$$ is exact if $$\frac{\partial N}{\partial y}=\frac{\partial M}{\partial x}$$
So re-writing the above differential equation as
$$
(2x-y\sin(2x))dx - (\sin^2x-2y)dy
=0$$
we can see that $$\frac{\partial N}{\partial y}=-\sin(2x)=\frac{\partial M}{\partial x}$$
so it is in fact exact.
