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Math Help - Partial differential equations

  1. #1
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    Partial differential equations

    Given u(x,y) = ф(3x-2y)
    (ф is an arbitrary function) find a PDE for u. Im just not sure how to start this question, any suggestions?
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  2. #2
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    Quote Originally Posted by mel240 View Post
    Given u(x,y) = ф(3x-2y)
    (ф is an arbitrary function) find a PDE for u. Im just not sure how to start this question, any suggestions?
    I guess you could do something like this

    Au_{xx}+Bu_{yy}+Cu_{x}+Du_{y}+Fu=0

    A, B, C, D, E, F are constants.
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  3. #3
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    Quote Originally Posted by mel240 View Post
    Given u(x,y) = ф(3x-2y)
    (ф is an arbitrary function) find a PDE for u. Im just not sure how to start this question, any suggestions?
    You'll notice that

    \dfrac{\partial u}{\partial x} = 3\phi'(3x-2y)

    \dfrac{\partial u}{\partial y} = -2\phi'(3x-2y)

    Now, can you think of a linear combination of these two to give you zero?
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