An interesting ODE perhaps?

gvk

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

amcavoy

Quote by gvk

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

Maybe convert to polar coodinates? That x²+y² wants to be r². Maybe not though

Alex

saltydog

Quote by gvk

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

I tend to look at it this way:

[tex](y^2-yx^2)dx-(xy^2+x^3)dy=0[/tex]

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

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gvk	An interesting ODE perhaps? Tweet Very simple in writing, but hard to solve: [tex] x*\frac{dy}{dx}=(y^2-y x^2)/(y^2+x^2)[/tex]