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Math Help - Determine whether the given function satisfies Laplace's equation

  1. #1
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    Determine whether the given function satisfies Laplace's equation

    f(x,y)=cos(x)sin(-y)

    What exactly do I have to do? From wikipedia it seemed like all I had to do to show that an equation satisfies Laplace's equation is show that:

    \frac{\partial f^{2}}{\partial x^{2}}+\frac{\partial f^{2}}{\partial y^{2}}=0

    Is this correct?

    If this is correct, please check my solution for the above function:

    \frac{\partial f}{\partial x}=-sin(x)sin(-y)+0

    \frac{\partial f}{\partial y}=0-cos(-y)cos(x)

    \frac{\partial f^{2}}{\partial x^{2}}=-cos(x)sin(-y)+0

    \frac{\partial f^{2}}{\partial y^{2}}=0+sin(-y)cos(x)

    \frac{\partial f^{2}}{\partial x^{2}}+\frac{\partial f^{2}}{\partial y^{2}}=-cos(x)sin(-y)+cos(x)sin(-y)=0

    Therefore, the equation satisfies Laplace's equation.
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  2. #2
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    That's correct.
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  3. #3
    MHF Contributor

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    By the way, "sine" is an odd function so you could have simplified this a little by writing f(x, y)= - cos(x)sin(y).
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