6. Consider the IBVP for the heat equation: ut(t, x) = Uxx (t, x), u(t,0) = 0 = u(t, π), u(0,x) = f(x) (a) Assume u(t, x

[answerhappygod]

1 (55.43 KiB) Viewed 10 times

6. Consider the IBVP for the heat equation: ut(t, x) = Uxx (t, x), u(t,0) = 0 = u(t, π), u(0,x) = f(x) (a) Assume u(t, x) = v(t)w(x) and derive the boundary value problem for w(x). (b) Find all solutions to the BVP from part (a). (c) Verify that for each n E N, un(t, x):= e-n²t sin(nx) is a solution to the heat equation. (d) Find a solution to the IBVP with f(x) = 3 sin(x) + sin(4x) (e) Find a solution to the IBVP with f(x) : - { *- = 0≤x≤π/2 π-x π/2≤x≤ π