# An interesting ODE perhaps?

Very simple in writing, but hard to solve:
$$x*\frac{dy}{dx}=(y^2-y x^2)/(y^2+x^2)$$
:tongue2:

gvk said:
Very simple in writing, but hard to solve:
$$x*\frac{dy}{dx}=(y^2-y x^2)/(y^2+x^2)$$
:tongue2:
Maybe convert to polar coodinates? That x2+y2 wants to be r2. Maybe not though

Alex

saltydog
Homework Helper
gvk said:
Very simple in writing, but hard to solve:
$$x*\frac{dy}{dx}=(y^2-y x^2)/(y^2+x^2)$$
:tongue2:

I tend to look at it this way:

$$(y^2-yx^2)dx-(xy^2+x^3)dy=0$$

but are unable to proceed. It's not exact, can't make it exact, and can't come up with any differentials by inspection.