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Math Help - partial differential equation satisfied by u(x,y)

  1. #1
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    partial differential equation satisfied by u(x,y)

    Let f : R \rightarrow R be differentiable and define u: R^2 \rightarrow R
    by u(x,y) := e^{x sin y}f(x - y) show that u satisfies the partial differential equation
    du/dx + du/dy= (sin y + x cos y)u ?
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  2. #2
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    \displaystyle{\frac{du}{dx} = \sin y\ e^{x \sin y} f(x-y) + e^{x \sin y} f'(x-y) \frac{df}{dx}}

    Similarly for \frac{du}{dy}, then add the two, obviously... pic in a mo.



    ... where (key in spoiler) ...

    Spoiler:


    ... is the product rule. Straight continuous lines differentiate downwards (integrate up) with respect to either x or y.

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    Last edited by tom@ballooncalculus; February 21st 2011 at 05:09 AM. Reason: typo
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