I've really spent a long time struggling with these.

The first one is finding the similarity solutions of

$\displaystyle \frac{\partial u}{\partial t} = x\frac{\partial^2 u}{\partial x^2}$

using the similarity variable $\displaystyle n = xt^a$, where a is a constant I have to determine all possible values of

The other problem is solving Laplace's equation

$\displaystyle \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2}=0$

using the similarity variable $\displaystyle n=xy^a$, where a is a constant I have to determine all possible values of