- #1

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**1. Solve the wave equation u_(tt) = 4u_(xx) on the interval [0, π] subject to the**

conditions

u(x, 0) = cos x, u_t(x, 0) = 1, u(0, t) = 0 = u(π, t).

conditions

u(x, 0) = cos x, u_t(x, 0) = 1, u(0, t) = 0 = u(π, t).

## Homework Equations

**3. Hello. This appears to be a common separation of variables question. Only problem is after using the boundary conditions and initial conditions, I am left with an unknown constant.**

So, after using 2 b.c. and first i.c. I'm left with U=∑_(n=1)^(n=∞)▒〖E_n Sin(nx)Cos2nt〗+F_n/2n Sin(2nt)Sin(nx)

The problem is when i use my last i.c. this tells me the value of constant E but I'm left with F!

So, after using 2 b.c. and first i.c. I'm left with U=∑_(n=1)^(n=∞)▒〖E_n Sin(nx)Cos2nt〗+F_n/2n Sin(2nt)Sin(nx)

The problem is when i use my last i.c. this tells me the value of constant E but I'm left with F!