Partial Differentials and wave equation.

[hhhmortal]

Homework Statement

How can I find out if a function is a solution of a wave equation such as:

(a) xt
(b) log(xt)
(c) x² + c²t²

The Attempt at a Solution

Is it simply differentiating the funtion with respect to 'x' twice and equating this to the product of 1/c² and differentiating the function twice with respect to 't'?

I tried doing it for part (c) and I got 1=1 which means its allowed I guess. As for part (a) I got 0=0 which i suppose it isn't?

 

[HallsofIvy]

Yes, just plug each function into the wave equation and see if they satisfy it: for each function, f, find f_xx and f_tt and see if they satisfy $f_{xx}= (1/c^2) f_{tt}$

 

[hhhmortal]

Ok, thanks, most of the time they seem to be 1=1 or 0=0 hence satisfying and not satisfying the wave equation i suppose..thanks again!