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Math Help - quasilinear pde

  1. #1
    Junior Member
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    Jun 2008
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    quasilinear pde

    I have to solve the following quasilinear equation using the method of characteristics:

    x u_x + y u_y +yu=xy
    u|_{y=x^2}=sin x

    \frac{dx}{dt}=x gives me ln x=t + c_1
    \frac{dy}{dt}=y gives me ln y=t+c_2

    But what do I do with \frac{du}{dt}=xy - yu?

    Thank you.
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  2. #2
    Junior Member
    Joined
    Jun 2008
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    Anyone? Please, it's really confusing and I need to understand it in order to go on..
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