Module for Linear First Order Differential Equations

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

Preliminaries.

    We wish to solve the first order linear D. E. with a given I. C.   

    ,  

the integrating factor is  .  Multiply each term by the integrating factor and get  

    .  

Observe that the left side of the above equation is a "perfect derivative" of the product   .  
This permits us to write the differential equation as follows.  

    .  

Integrate both sides and get  

    .
    
Therefore, the general solution is

    .

Example 1.  Use Mathematica to solve the first order linear D. E. with the given I. C.   

           with   y(0) = -2.

Plot the solution over the interval  [0, 3].

Example 2.  Use Mathematica to solve the first order linear D. E. with the given I. C.   

           with   y(0) = 1.

Plot the solution over the interval  [0, 3].

Example 3.  Solve the  first order linear differential equation  .  

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