# Non-linear ODE

1. Feb 8, 2012

### gizsim

Hi.
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!

2. Feb 8, 2012

### timthereaper

There might not be an analytical solution for that PDE.

3. Feb 10, 2012

### kai_sikorski

Are there any small parameters in the problem?

If for example p1/p0 << 1 and p2/p0 << 1 then you might be able to find a solution using regular perturbation theory.

4. Feb 17, 2012

### anirudhnandan

How to solve a equation of this kind

T' = a*(T^4 - r^4) + b*(T^4 - s^4) + P*(1 - eta(T))

The above equation is driving me nuts... the 'eta' is a function of T(Temperature) and initial value of T is known.
Say at t = 0 T is 298