Question

8. Find the solution of the following PDE: utt − 9uxx = 0 u(0, t) =...

8. Find the solution of the following PDE:

utt − 9uxx = 0
u(0, t) = u(3π, t) = 0
u(x, 0) = sin(x/3)
ut (x, 0) = 4 sin(x/3) − 6 sin(x)

9. Find the solution of the following PDE:

utt − uxx = 0

u(0, t) = u(1, t) = 0

u(x, 0) = 0
ut(x, 0) = x(1 − x)

10. Find the solution of the following PDE:

(1/2t+1)ut − uxx = 0

u(0,t) = u(π,t) = 0
u(x, 0) = sin(x) + 3 sin(2x)

Please answer all three, will give good rating as soon as possible

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