Homogenous diff equations of the form P(x,y)dx + Q(x,y)dy = 0 thank you for taking the time to help me out. I am reviewing a past test while looking in my book to try to figure out how to do this. I understand the way to solve these types of problems, I only get stuck at determining whether they are homogenous or not. For example: $(x^2 + y^2)dx + (xy) dy=0$ How do I know it is homogenous? All the book says is that it is homogenous of degree 2. I understand that once I am able to identify that, then I set $y=xv$ and the rest I understand, but how do I distinguish problems like this? Another example from my last test, $(xy^2 - 2x^3)dy=(yx^2 + y^3)dx$

Based on my research session (aka studying for finals), I finally found a source that put it this way:

A function G(x,y) is homogenous of degree n if: $G(tx,ty) = t^nG(x,y)$

Hence, if by replacing x and y with $\lambda x$ and $ \lambda y$ You yield the same function being multiplied by some power of lambda ($\lambda^n$) then you know the equation is homogenous with degree n.