Transform the following equation to the form$\displaystyle v{\xi}{\eta} = cv$, where c is a constant,

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

by introducing the new variables $\displaystyle v = u\exp^{-(a{\xi} + b{\eta})}$ , 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$\displaystyle \mbox{ u{\xi}{\eta}}$ 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$\displaystyle v{\xi}{\eta} = -(1/16)v$

I don't know how to work this out.

Please help.