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C2-solutions to a diff.equation.

  1. Dec 14, 2014 #1
    I have the following problem:
    Calculate all the C2-solutions z(x,y) to the differential equation:


    with the following constraint: dQaYDIt.png
    by making the substitution u=xy, v=x


    I've begun slightly but this doesn't take me far..

  2. jcsd
  3. Dec 14, 2014 #2


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    Homework Helper

    Start by working out what the differential operators [itex]\frac{\partial}{\partial x}[/itex] and [itex]\frac{\partial}{\partial y}[/itex] are in terms of [itex]u[/itex], [itex]v[/itex] and the differential operators [itex]\frac{\partial}{\partial u}[/itex] and [itex]\frac{\partial}{\partial v}[/itex]. From these you can find expressions for the second-order operators.

    Now substitute these expressions into the original PDE, and tidy up the result. You should find that most of the terms cancel.
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