Let u be a constant. Prove that u=sin(x-at)+ln(x+at) is a solution to the wave equation (u_tt=a^2*u_xx)..?

Question

turingtest · Answer

plug it in and differentiate

turingtest · Answer

what are $u_{xx}$ and $u_{tt}$ ?

anonymous · Answer

Oh, hahaha I was looking at this way wrong. So what I have to do are take the second partial derivatives of it and just plug them in, right?

turingtest · Answer

yup. it's easy to over-think problems when they're worded all fancy I know :P

anonymous · Answer

Hahaha thank you for all of your help, it is greatly appreciated :)

anonymous · Answer

So, I got f_x=2x+ky
f_y=2y+kx.
I then did this:
f_x=2x+ky=0
f_y=2y+kx=0
I solved for y and substituted y in the f_x equation with the value I got. I then had:
y=kx/2
2x+ky=0------>2x+k(kx/2)
I then proceeded to solve for x and got...
x(4+k^2)=0
So...x=0?
I then plugged 0 into the y= equation
y=k(0)/2
and got y=0.
Hence (0,0) is a critical point, yes?
What's my next step?

anonymous · Answer

SORRY, WRONG QUESTION