(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Solve, [tex]u_{t} = u_{xx}c^{2}[/tex]

given the following boundary and initial conditions

[tex]u_{x}(0,t) = 0, u(L,t) = 0[/tex]

[tex]u(x,0) = f(x) , u_{t}(x,0) = g(x)[/tex]

2. Relevant equations

[tex]u(x,t) = F(x)G(t)[/tex]

3. The attempt at a solution

I solved it, I am just not sure if it is right.

[tex]u(x,t) = \sum_{n=1}^\infty(a_{n}cos(\lambda_{n}t) + b_{n}sin(\lambda_{n}t))cos((n-\frac{1}{2})\frac{\pi}{L}x)

, \lambda_{n} = (n-\frac{1}{2})\frac{\pi}{L}c [/tex]

[tex]a_{n} = \frac{2}{L}\int_0^L f(x)cos((n-\frac{1}{2})\frac{\pi}{L}x)dx,

b_{n} = \frac{4}{(2n-1)c\pi}\int_0^L g(x)cos((n-\frac{1}{2})\frac{\pi}{L}x)dx

[/tex]

Can someone please verify this for me?

Thanks in advance,

KEØM

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# 1-D Wave equation with mixed boundary conditions

**Physics Forums | Science Articles, Homework Help, Discussion**