Module for the Laplace Transform Solution of an O. D. E.

Numerical Methods for O. D. E.  using Mathematica. (c) John H. Mathews, 2003

Background.

    Laplace transforms are useful in solving initial value problems for ordinary differential equations and systems of ordinary differential equations. In this exercise we explore the method of using Laplace transforms. First load Mathematica's built in "LaplaceTransform" subroutine package.

Example 1.  Use Laplace transforms to solve the initial value problem

       with  .

Example 2.  Use Laplace transforms to solve the initial value problem

      with  ,  
    
and plot the solution over the interval  .  

Example 3.  Solve the initial value problem

      with  .  

Example 4.  Use Laplace transforms to solve the initial value problem  

      with  ,  
    
and plot the solution over the interval  .  

Example 5.  Use Laplace transforms to solve the initial value problem for the system of D.E.'s  

        with       
    
and plot the solution for  .  

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