Example 10.  Plot the solutions to the D. E.    in Example 9
that have the following initial conditions  x[0] = 4, 5, 6, 7, 8.

Solution 10.

We shall use the technique where we solve    for  .
You will get some warning messages from Mathematica, ignore them.  Hang in there !

Replace the values    for the constant c[1],
and form the functions we wish to plot.

Make them look nicer.  

Graph these solutions.

Observe.  The family of functions
tend to the constant function    as  .  

(c) John H. Mathews 2004