Question

Show that (x^2+3xy+y^2)dx-x^2*dy=0 is homogeneous.

Answer 1

Do you mean "exact"?

Answer 2

What do you mean?

Answer 3

I could be mistaken, but some differential equation questions give you a function of \(x,y, \text{ and }y'\) on one side of the equation and set it equal to 0.

Something that looks like this:
\[M(x,y)+N(x,y)\frac{dy}{dx}=0\]
If you can show that \(\dfrac{\partial M}{\partial y}=\dfrac{\partial N}{\partial x}\), then you have an exact equation.