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Solve $\displaystyle\frac{dy}{dx}=(x^2+y^2)^2$

Any hints for me the solve the problem??

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5  
What is $F$? A Lyapunov function? –  copper.hat Nov 15 '12 at 16:54
    
We can find y(x) or x(y) here, but what is F(x,y)? –  Miguel Dovale Nov 15 '12 at 16:54
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@cwk709394 - that fact that you haven't accepted any answers to the other 5 questions you've asked on math.stackexchange might be a disincentive for people to answer your question here. The "accept answer" button is just below the arrow down button on the answer; might be a good idea to go over your previous questions and accept some answers - looking at your past questions, it seems there were some acceptable answers given. :) –  James Fennell Nov 15 '12 at 17:21
    
Sorry about that. I corrected my question now –  cwk709394 Nov 16 '12 at 1:47
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May want to consider accepting questions for which people have provided a sufficient answer –  Thomas Nesbitt Nov 16 '12 at 2:57

1 Answer 1

up vote 2 down vote accepted

$\dfrac{dy}{dx}=(x^2+y^2)^2$

$\dfrac{dy}{dx}=y^4+2x^2y^2+x^4$

This belongs to a "Chini-like" equation as mentioned here and which is more complicated than Abel equation of the first kind.

I still don't know whether existing a substitution so that $y^2$ term can be eliminated and keeping $y^3$ term still vanished, leading it exactly belongs to a Chini equation.

It still don't know whether existing method can solve Chini equation generally, while Abel equation of the first kind eventually can be solved generally starting in 2011 August, see this for details.

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