Example 2.  Use Mathematica's procedure DSolve to get an analytic solution for the differential equation  [Graphics:Images/TaylorDEMod_gr_51.gif]  with initial condition  [Graphics:Images/TaylorDEMod_gr_52.gif]  over the interval  [Graphics:Images/TaylorDEMod_gr_53.gif].
Solution  2.

First, Remove any instance of y.   
But make sure y is not empty when you do it.

[Graphics:../Images/TaylorDEMod_gr_54.gif]

Then solve the D. E. with given I. C.  

[Graphics:../Images/TaylorDEMod_gr_55.gif]

[Graphics:../Images/TaylorDEMod_gr_56.gif]

[Graphics:../Images/TaylorDEMod_gr_57.gif]

[Graphics:../Images/TaylorDEMod_gr_58.gif]

[Graphics:../Images/TaylorDEMod_gr_59.gif]
[Graphics:../Images/TaylorDEMod_gr_60.gif]

Compare the two graphs.  

[Graphics:../Images/TaylorDEMod_gr_61.gif]

[Graphics:../Images/TaylorDEMod_gr_62.gif]

[Graphics:../Images/TaylorDEMod_gr_63.gif]

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003