Example 12.  Solve the I.V.P.  .    Compute a Taylor  series solution of order n=4 solution to the I.V.P.

Solution  12.

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

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

Third, use the subroutine to compute the set of points and store them in the variable taylorset.  Then plot this set of points using the built in Mathematica subroutine ListPlot.  

Animation 1.  ( Taylor's method of order 4  Taylor's method of order 4 ).  Internet hyperlink.

(c) John H. Mathews 2004