Question

My textbook says \[M(x,y)dx + N(x,y)dy = 0\] is homogenous if \[M(tx,ty)=t ^{\alpha}M(x,y)\] and \[N(tx,ty)=t ^{\alpha}N(x,y)\]. What does that mean?
I know that if the function equals \[F=x/y\] then it's homogenous. How do those two rules relate?

Answer 1

Basically, how do you test if a function is homogenous?