Example 12.20.  Solve the initial value problem  

                                 

Explore Solution 12.20.

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

Use the facts that    and  construct y[t].

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.

Notice that the derivative of the unit step function involves the  Dirac delta function.

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

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