Write a program for solving the ODE just considered and for jointly graphing input and output of an initial value problem involving that ODE. Apply the program to Probs. 7 and 11 with initial values of your choice.

Data from Prob. 7

Find a general solution of the ODE y" + ω²y = r(t) with r(t) as given. Show the details of your work.

r (t) = sin t, ω = 0.5, 0.9, 1.1, 1.5, 10

Data from Prob. 11

Find a general solution of the ODE y" + ω²y = r(t) with r(t) as given. Show the details of your work.