Example 8.   Use the Modified Euler Method to find numerical solutions to the D. E.  .  

Solution 8.

The solution curves with the initial conditions    can all be computed over the interval  .  
However the solution curves with the initial conditions      must be computed over smaller intervals,
for instance the intervals   .

Now all the solution curves can be shown on one graph.

This is the same as the graph that was obtained in Example 6.

(c) John H. Mathews 2004