# Solving partial differential equations 2

So the partial differential equation is:

$$\frac{\partial h}{\partial t} =\frac{\partial}{\partial x} (\frac{1}{3}h^3 \frac{\partial h}{\partial x})$$

and $$h = t^\alpha f(\xi)$$, where $$\xi=\frac{x}{t^\beta}$$

I want to determine a relationship between constant $$\alpha$$ and $$\beta$$.

So I plug the $$h$$ into the original equation which gives me a mess. Am I doing something wrong?

• Well, plugging $h$ into the equation seems to be the most natural thing to do. You got a mess? Maybe you actually were supposed to make some sense out of it. Or maybe you did something wrong. What exactly? How are we to know? – Ivan Neretin May 9 at 12:46