(adsbygoogle = window.adsbygoogle || []).push({}); Assumed solution for the Laplace EQUATION??

The book I'm using says that the method of separation of variables is a must when solving the Laplace equation. OK, well they ASSUME that the solution looks like

V(x,y,z)=X(x)*Y(y)*Z(z)

but why can't they assume a solution of

V(x,y,z)=X(x) + Y(y) + Z(z)?????

When performing the[itex]\nabla \bullet [/itex]([itex]\nabla[/itex]V)operation, the difference is that their assumed solution leads to[1/X(x)]* d, while what I'm proposing will lead to just^{2}[X(x)]/dx^{2}= -k_{x}^{2}d^{2}[X(x)]/dx^{2}= -k_{x}^{2}

Since what I'm proposing is easier, why would that be the one used?

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

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

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

# Assumed solution for the Laplace EQUATION?

**Physics Forums | Science Articles, Homework Help, Discussion**