Example 5.  Form the desired solution to Example 1.

Solution 5.

Finally, the desired solution x(t) is the linear combination  

     .   

For this example we have    and we can locate   in    and   in  .  
Since the desired solution is  ,  these ordinates are a linear combination of the two previously computed solutions.

The points (t, x(t)) are now formed.

Now we can plot the solution.

The first point is

The last point is

(c) John H. Mathews 2004