Show us what you've tried so that we can help.
I've really spent a long time struggling with these.
The first one is finding the similarity solutions of
using the similarity variable , where a is a constant I have to determine all possible values of
The other problem is solving Laplace's equation
using the similarity variable , where a is a constant I have to determine all possible values of
for the second one I managed to solve by the normal method of writing u as a product of a function of x only and a function of y only and working through to get:
for constants k and c subscript 1-4
but i'm not sure how to write up a solution using their similarity variable, or how to be sure how i've found all the possible constants a
Yeah you should find the partial derivatives in terms if the similarity varibles and the other varibles then (i suggest combining to find one co-efficient in front of f' ) attempt to choose alpha such that you have an ode with constant co-efficients or in terms of the similarity vairable, I think you get 2 values forth diffusion equation and three for laplace