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In the course of trying to solve the field equations of a physical system, within some assumptions about its symetry, i managed to get a non-linear ODE involving only a single function of one variable, but still rather tough to handle :

In the equation, x=x(r) is the unknown function to find, and p0, p1, p2 are KNOWN algebraic functions of r (that i didn't take the time to write down here, but are not too complicated functions).

p0*(x''-x'²) + x'(x²+2x) (-/+) p1*x^4 + p2*x³ - p2*x² (+/-) p1*x = 0

Do you guys have any ideas of how i could manage to obtain any analytic solution for x(r)?

I can't find any help, because its not a categorized equation (Ricatti, Abell, ...)

Thank you so much for your help!

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# Non-linear ODE

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