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Math Help - Find a PDE that satisfied by all the functions of the form

  1. #1
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    Find a PDE that satisfied by all the functions of the form

    Find a PDE that satisfied by all the functions of the form

    u=f(x^2-y^2)

    f can have as many derivatives as needed.

    How would I go about doing this?

    Thanks.
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    Quote Originally Posted by dwsmith View Post
    Find a PDE that satisfied by all the functions of the form

    u=f(x^2-y^2)

    f can have as many derivatives as needed.

    How would I go about doing this?

    Thanks.
    Dear dwsmith,

    u=f(x^2-y^2)

    \dfrac{\partial u}{\partial x}=2x\dfrac{\partial f}{\partial(x^2-y^2)}

    \dfrac{\partial u}{\partial y}=-2y\dfrac{\partial f}{\partial(x^2-y^2)}

    Eliminate \dfrac{\partial f}{\partial(x^2-y^2)} from these two equations and you will get the required partial differential equation.
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