Assignment:
Solve the following string equation problem
utt = 1/4 uxx, 00,
u(0, t) = 0, u(1,t)=0, t>0
1/2 x, 0< x<1/2
u(x,0) =
1-x, 1/2
ut (x,0) = 0
Solve using separation of variables and D'Alembert. Show solutions in detail.
Graph both solution u(x, t) for t = 0, 1, 2, 4.