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