The question is Solve the one dimensional wave equation

on , subject to the conditions

,

well i started it, but im not sure if this is right coz i don't really understand wave or heat equations SIGH...

and

Case 1let

Using Auxilliary Equations:

So

And

As

Therefore, and

Therefore, no solutions...

Case 2

Auxilliary Equations ,

Therefore,

As

So

Therefore, no solution as

Case 3as

Auxilliary Equation: \

So

So

Therefore, and

Thus,

Now Im lost, am i doing it right so far, if so, then how do i go about completing this, coz i have no idea what to do now.. Thank you