# Wave equation with initial and boundary conditions.

1. May 14, 2010

### Mech.Obaid

Hallo Every one,

1. The problem statement, all variables and given/known data

y(x,t)=sin(x)cos(ct)+(1/c)cos(x)sin(ct)

Boundary Condition:

y(0,t)=y(2pi,t)=(1/c)sin(ct) fot t>0

Initial Condition :

y(x,0)=sin(x),( partial y / Partial t ) (x,0) = cos(x) for 0<x<2pi

show that y(x,t)=sin(x)cos(ct)+(1/c)cos(x)sin(ct) satisfies the one dimensional wave equation together with boundary and initial conditions.

Please any one can clearify the question for me so i can solve it.

Last edited: May 14, 2010
2. May 14, 2010

### Mech.Obaid

Just i want to know how i can prove that the given function satisfies the Boundary condition and initial condition.

3. May 14, 2010

### Cyosis

The boundary and initial conditions have been given. Now you just have to plug the appropriate values for x and t belonging to said conditions into your solution.

4. May 14, 2010

### Mech.Obaid

iam not trying to slove the boundary value problem

i want to prove that the given function satisfy the boundary and initial condition.

5. May 14, 2010

### Cyosis

Yep and post #3 gave you the method as to how to do just that.

Hint: what is the x value that belongs to the given boundary condition?

6. May 14, 2010

### Mech.Obaid

thanks Cyosis

Just i concentrate and i solve it