Example 1.  Use Mathematica to solve the D. E.  .  

Solution 1.

Use the Mathematica's procedure  DSolve.

Caveat.  The general solution found by Mathematica (and Maple too) is for case (iii) only.  Is this a surprise ?  It is up to the reader to find proof for the formulas in cases (i) and (ii).

Warning.  This illustrates what happens when we use a computer symbolic algebra system such as Derive, Maple, Matlab, MACSYMA or Mathematica is used to find the "general solution."  Only one solution is found.  Furthermore, it might be the "least significant" of the three forms of the solution that exist.  However, luck is with us.  When numbers are used for the arbitrary constants, Mathematica will find the correct solution.  This "confusion" must be understood if a practicing mathematician is planning on using computer symbolic algebra systems such as Derive, Maple, Matlab, MACSYMA or Mathematica.

(c) John H. Mathews 2004