If we call [tex] U_{xx}= \partial _{x} \partial _{x} U [/tex] the second partial differential derivative so we have for the Laplace operator:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \nabla ^{2} U = U_{xx}+U_{yy}+U_{zz} [/tex] then let,s suppose we have the differential equation:

[tex] aU_{xx}+bU_{yy}+cU_{zz}+dU_{xy}+eU_{xz}+fU_{yz}=0 [/tex]

then my question is if we can use a linear transform to choose another coordinate system so the equation read: [tex] \nabla^{2} U=0 [/tex]

thanks.

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# Partial differential equation problem

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