Module for Exact Differential Equations

Numerical Methods for O. D. E.  using Mathematica. (c) John H. Mathews, 2003

Preliminaries.

    We wish to solve the exact D. E. with a given I. C.   

     ,  

it is necessary that   .

The general solution is a family of curves  f[x,y] = c, and the particular solution is an implicit curve ,  
where  .

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

        .

Example 2.  Use Mathematica to solve the exact D. E.  

        .

Example 3.  Solve the differential equation  

        .
        
3 (a)  Show that the given D.E. is exact.
3 (b)  Use the appropriate steps to construct a solution, the final result is to be displayed in the form .

Example 4.  Solve the exact differential equation  

        .  
        
4 (a)  Show that the given D.E. is exact.
4 (b)  Use the appropriate steps to construct a solution, the final result is to be displayed in the form  .  

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