Wave equation with initial and boundary conditions.

[Mech.Obaid]

Hallo Every one,

Homework Statement

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 anyone can clearify the question for me so i can solve it.

 

[Mech.Obaid]

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

 

[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.

 

[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.

 

[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?

 

[Mech.Obaid]

thanks Cyosis

Just i concentrate and i solve it