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?

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?

anonymous · Answer

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