In Problems 1 and 2, solve the heat equation (1) subject to the given conditions. Assume a rod of length L.
1. u(0, ) = 0, u(L, 1) = 0 Si, 02. u(0, 1) = 0, u(L, 1) = 0 u(x, 0) = x(L - x)
In Problems 1-6, solve the wave equation (1) subject to the given conditions.
4. u(0, 1) = 0, UTT, 1) = 0, > 0 atl=0 u(x, 0) = x(? – x2), cm = 0, 05. (0, 1) = 0, (1, 1) = 0, t> 0 u(x, 0) = X(1 — x), 0 = X(1 — x), 0
