I asked the professor about it and apparently it's just an equation he "thought of off the top of his head" to see if we could solve it, and then told us to do it for homework, lol. Do you have any clue how to go about getting to that "very complicated inverse function" for the solution?
Problem and Equation: Solve dy/dx=-y/(x^2+y)
Put into standard form, this is ydx+(x^2+y)dy=0
The only ways of solving differential equations that I currently know are when they are either linear (which this is not), separable (this is also not), or exact (ditto), and I vaguely know about...