71 Find the solution of the PDE that satisfies the given IC

Find the solution of the PDE that satisfies the given IC and BCs. Use CAS to evaluate integrals. Reproduce the IC by plotting the solution at t = 0. Reproduce the IC by plotting the solution at t = 0 by including the Lanczos factor. Show how the solution progresses at t = 0.02 and t = 0.2 units of time. Report the steady-state solution as t rightarrow infinity. IC: u(x, 0) = 25sin(pi x). IC: u(x, 0) = 25 x sin(pi x). The IC is u(x, 0) = 25 x^2 sin(pi x). The IC is u(x, 0) = 25 x^2.

Solution

one dimensional heat equation alpha^2 u_xx=u_t

_{will have initial condition as u(x,0)=f(x)=25x^2}