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Math Help - Classification of second order linear equations

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    Question Classification of second order linear equations

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

    uxx-uyy+3ux-2uy+u = 0

    by introducing the new variables  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 \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  v{\xi}{\eta} = -(1/16)v

    I don't know how to work this out.
    Please help.
    Last edited by mrmaaza123; March 30th 2013 at 02:22 AM.
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