Transform the following equation to the form , where c is a constant,

u_{xx}-u_{yy}+3u_{x}-2u_{y}+u = 0

by introducing the new variables , where a and b are undetermined coefficients, also there is no 8203 in the question, i just don't know why its hanging along.

The way i tried to do it was, by first transforming this equation into the canonical form in terms of and then i tried to get rid of it using the given relation, but it didn't seem to help much.

The answer to this question is

I don't know how to work this out.

Please help.