ODE: Second Order - Symbolic Solution

The ODE is

Two solutions are presented for cases (a) and (b).  The solutions are shown graphically
Output in the Command Window
(The ASCII outputt does not copy well to HTML because of the tag properties.  Please check actual solution in Command window as these may have editing error)
Natural Motion -Case (a)
          10   1/2                         1/2                                            1/2
          -- 21    exp(-2 t) sin(21        t) + 5 exp(-2 t) cos(21        t)
          21
 

Forced Motion - Step - Case (b)
                          1/2                                 1/2                                      1/2
        2 + 2/7 21         exp(-2 t) sin(21    t) + 3 exp(-2 t) cos(21           t)