Example 2.  Use Picard iteration to find the solution of the I.V.P.  

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Solution 2.

First define the function    and the initial condition    by typing:

Picard iteration for generating the first six approximations is started with the Mathematica command:

    Techniques from calculus can be used to find the solution  ,  and it is easy to verify this fact using the rules of differentiation and a trigonometric identity .   

            

The first five terms of the Picard approximation are the same as the Maclaurin series for  .

(c) John H. Mathews 2005