Q: Differential equation involving a rational function with $\cos(xy)$ and $\sin(xy)$ How to solve this differential equation?
$$\frac{ dy}{dx}= \frac{ 3x^2 \cos⁡(xy)-x^3 y\sin(xy)+4x}{x^4 \sin⁡(xy)-8y}$$
The $xy$ inside both sine and cosine are really throwing me off, not even sure which solution to use. Help! 

A: When $dy/dx$ is equated to an complicated fraction in which the numerator and denominator have some similar terms, you should suspect an exact ODE. Rewrite in the form of differentials, $Mdx+Ndy=0$
$$ (3x^2 \cos⁡(xy)-x^3 y\sin(xy)+4x)dx  + (8y-x^4 \sin⁡(xy)) dy = 0$$
and think if this looks like the differential of something... something with $x^3\cos xy$, per chance? 
