Question

Find a solution to the following partial differential equation that will also satisfy the boundary conditions.
d^2 u/dt^2-81*d^u/dx^2=0
u(0,t)=u(4pi,t)=0
u(x,0)=36sin(x/4)
du/dt(x,0)=36sin(x/4)-180sin(4x)
Please help me ! and show me the steps. I really need to know how to do this problem. thank you so much for helping me.
The screen shot of the question is below. Please check. Thank you!

Answer 1

Here's a fairly short explanation on how to work this kind of problem out: https://docs.google.com/a/iwu.edu/viewer?a=v&pid=gmail&attid=0.1&thid=13e42c94e5ad91e9&mt=application/pdf&url=https://mail.google.com/mail/u/1/?ui%3D2%26ik%3D27bfc4ccdf%26view%3Datt%26th%3D13e42c94e5ad91e9%26attid%3D0.1%26disp%3Dsafe%26realattid%3Df_hfycx22c0%26zw&sig=AHIEtbSfyforI3M5jhs_SR_lHXOOdTHcRg

Skip down to section 4, as that's what you're looking for. I actually wrote this up for a class, so I should be able to explain anything you have trouble with.

Answer 2

It may be the case that you won't be able to open the link... I'll attach a pdf as well, once I find it.