Solve: $(2xy+e^x) dx + (x^2 y -\sin{y}) dy=0$
Clearly, the differential equation is not exact. After applying various methods to no avail, (including power series and Fourier expansion) I cannot see how to get to the solution (an approximating polynomial will do). Online tools are useless here too. Maybe treating it analytically is the only way.
Or does it have a simple solution which I am missing?