Example 12.23.  Use Laplace transforms to solve the initial value problem

                

Explore Solution 12.23.

Enter the initial conditions and the functions f[t] and F[s].  Then Laplace transform the D.E. and solve for Y[s]. Observe that a D.E. involving Y'[s] will arise in the computations.

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

Aside. For this problem, the solution involves a family of functions. We can use Mathematica/s to plot several solutions.

Remark.  For this differential equation there is a family of solutions.

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