# Laplace equation

fk378

## Homework Statement

Verify that the function u=1/(x^2 + y^2 + z^2)^2 is a solution of the 3-dimensional Laplace equation uxx+uyy+uzz=0

## The Attempt at a Solution

I know how to solve the partial derivatives, so I know that uxx=uyy=uzz for this problem. How can their sum equal 0?

lzkelley
are you sure its not ^3/2?

Homework Helper
are you sure its not ^3/2?

You mean ^(1/2), yes? 1/r is the Green's function for the Laplace equation.

fk378
Ah, yes, the function should read:
u=1/(x^2 + y^2 + z^2)^(1/2)

Can you explain how the sum of the partial derivatives should equal zero, if their individual expressions are equal and positive?

Homework Helper
Ah, yes, the function should read:
u=1/(x^2 + y^2 + z^2)^(1/2)

Can you explain how the sum of the partial derivatives should equal zero, if their individual expressions are equal and positive?

You said you know you to find the second derivatives. Then do it. The individual expression aren't 'equal and positive'. Tell me what is the second derivative u_xx? It has two terms which cancel when summed over x,y and z.

fk378
For u_xx I'm getting 3(x^2 + y^2 + z^2)^-(5/2)