Example 9.  Solve the I.V.P.  .  

Solution  9.

Compute the Taylor series solution based on 50 subintervals and plot the results.

First, enter the function    and create explicit formulas for    for  ,  respectively, which will involve  .  

Second, replace    with     and construct the implicit formulas    for  , respectively.  

Compute the Taylor series solution based on 100 subintervals and plot the results.
Observe that one fewer subinterval is computed for this case.

Compute the Taylor series solution based on 200 subintervals and plot the results.
Observe that four fewer subintervals are computed for this case.

(c) John H. Mathews 2004