Homework Help: Show that the function is a solution of the wave equation

1. Jul 17, 2015

robertmatthew

1. The problem statement, all variables and given/known data
Show that the function is a solution of the wave equation utt = a2uxx.

u = (t)/(a2t2-x2)

2. Relevant equations
Quotient rule
(f/g)' = (g*f ' - f*g') / g2

3. The attempt at a solution
I began with the first and second partials of u with respect to x:
http://imageshack.com/a/img661/7646/Xnbsd2.png [Broken]
I'm fairly confident that this part is correct, because I checked it with an online calculator.
Then I did the first partial of u with respect to t:
http://imageshack.com/a/img537/4254/5hYVrv.png [Broken]
Then the second partial:
http://imageshack.com/a/img537/7426/Xr15AC.png [Broken]

So I'm getting -utt = a2uxx. I've done this several times now, and I keep getting the extra negative sign in utt. I can't figure out where it's coming from; I'm sure it's some silly mistake with a dropped sign somewhere. I'd appreciate the help of anyone who could help me spot it.

Last edited by a moderator: May 7, 2017
2. Jul 17, 2015

RUber

*Edit* Sorry I misspoke on the initial response.
It looks like in your simplification of the second partial wrt t, you cancel a negative sign incorrectly.

Last edited: Jul 17, 2015
3. Jul 17, 2015

robertmatthew

Ah, I see it now. No idea why I kept thinking I could do that; I must have done this problem five or six times and did that every time. Thanks for your help!