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 andD'Alembert. Show solutions in detail. Graph both solution u(x, t) for t = 0, 1, 2, 4.
Provide complete and step by step solution for the question and show calculations and use formulas.