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

$\displaystyle u=f(x^2-y^2)$

f can have as many derivatives as needed.

How would I go about doing this?

Thanks.

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- Dec 25th 2010, 06:08 PMdwsmithFind a PDE that satisfied by all the functions of the form
Find a PDE that satisfied by all the functions of the form

$\displaystyle u=f(x^2-y^2)$

f can have as many derivatives as needed.

How would I go about doing this?

Thanks. - Dec 25th 2010, 08:08 PMSudharaka
Dear dwsmith,

$\displaystyle u=f(x^2-y^2)$

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

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

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