Problem statement: If where , for prove that

This is my approach:

So

It seems I made an major error somewhere or I have conceptual problems.

Help me!

Thank you

Printable View

- Feb 4th 2013, 07:17 AMpatzerDoes the function u match the differential equation
**Problem statement**: If where , for prove that

**This is my approach**:

So

It seems I made an major error somewhere or I have conceptual problems.

Help me!

Thank you - Feb 4th 2013, 02:19 PMjohngRe: Does the function u match the differential equation
Yes, you made an error in the calculation of the 2nd partials. Here's the situation: you have a function r(x,y,z) and a function u=f(r) (in your case 1/r). So you want the partials of u w.r.t. x , y and z. The first partial u

_{x}=f'(r(x,y,z)__times__r_{x}is used correctly. But the second partial is:

, using the__product__rule.

If you do this (replacing occurrences of r) you get:

Similarly for the other 2nd partials. It is then easy to see that Laplace's equation is satisfied. - Feb 4th 2013, 02:26 PMpatzerRe: Does the function u match the differential equation
Thank you John