An interesting ODE perhaps?


by gvk
Tags: interesting
gvk
gvk is offline
#1
Oct8-05, 01:00 PM
P: 83
Very simple in writing, but hard to solve:
[tex] x*\frac{dy}{dx}=(y^2-y x^2)/(y^2+x^2)[/tex]
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amcavoy
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#2
Oct8-05, 01:05 PM
P: 669
Quote 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
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#3
Oct9-05, 03:41 PM
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Quote 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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