Example 12.15.  Solve the initial value problem  

               

Explore Solution 12.15.

Enter the initial conditions and the functions f[t] and F[s].  Then Laplace transform the D.E. and solve for Y[s].

Using the known Laplace transforms   the solution f[t] is the linear combination  .  

Aside. We can check this with Mathematica's  result using the LaplaceTransform package.

Aside. We can substitute y[t] into the D.E. and verify it is a solution.

Aside. We use Mathematica/s DSolve package to solve the D.E. and plot the solution.

(c) 2006 John H. Mathews, Russell W. Howell