# Thread: Help with solving a second order non-linear pde

1. ## Help with solving a second order non-linear pde

Hello!

I have a second order non-linear partial differential equation. I've tried to solve it by using a transformation of variables, without success so far...

It can be that my equation does not have an analytical solution, but i'm not sure. Can anyone help me please?

I attached the equation in a pdf file. I'm sorry, i got a LATEX error trying to insert the equation into the post.

Thank you very much!

2. ## Re: Help with solving a second order non-linear pde

The PDE is question is

$\displaystyle Dx^2f_{xx} + C x f_x + B\left(f_xf_y^{\beta}\right)^{\frac{1}{1-\beta}} + A f_x^{\frac{\alpha - 1}{\alpha}} = 0$.

A few questions. Are $\displaystyle A-D$ constant? Is $\displaystyle \alpha$ and $\displaystyle \beta$ constant? Are there are particular values of $\displaystyle \alpha$ and $\displaystyle \beta$ that are of interest? What if $\displaystyle \alpha = 0$ or $\displaystyle \beta = 1$? Do you limiting PDEs for these?

3. ## Re: Help with solving a second order non-linear pde

Thank you very much for your reply,

Actually, $\displaystyle A-D$ are constants. Also $\displaystyle \alpha$ and $\displaystyle \beta$ are constants, and are expected to be less than zero.

Thank you again!

Alejandro