For problems 68 through 73, 6. Find the solution of the PDE that satisfies the given IC and BCs. Use CAS to evaluate integrals. 7. Reproduce the IC by plotting the solution at t=0. 8. Reproduce the IC by plotting the solution at t=0 by including the Lanczos factor. 9. Show how the solution progresses at t=0.02 and t=0.2 units of time. 10. Report the steady-state solution as t→oo. 68. IC: u(x,0)=25 sin(x). 69. IC: u(x,0)=25x sin(x). 70. The IC is u(x, 0) = 25x² sin(x). 71. The IC is u(x,0)=25x². 162 62 du du Consider the second-order linear, and homogeneous PDE 0 over the domains ax² at 0<x<1 and 1>0, where x is space and t is time. The homogeneous Dirichlet BCs at x=0 and x = 1 are u(0,1)=0; u(1,1)=0; 1>0.