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.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Partial differential equation problem

Loading...

Similar Threads - Partial differential equation | Date |
---|---|

A How to simplify the solution of the following linear homogeneous ODE? | Feb 18, 2018 |

I Substitution in partial differential equation | Jul 8, 2017 |

A A system of partial differential equations with complex vari | Jul 6, 2017 |

**Physics Forums - The Fusion of Science and Community**