Example 5.  Plot some more solutions to the D. E.  [Graphics:Images/HarvestingModelMod_gr_105.gif]  in Example 3
Plot those that have the following initial conditions  [Graphics:Images/HarvestingModelMod_gr_106.gif].

Solution 5.

Use the general solution that was constructed in example 4.

[Graphics:../Images/HarvestingModelMod_gr_107.gif]

[Graphics:../Images/HarvestingModelMod_gr_108.gif]

Solve for the constant C[1] to make the initial conditions  [Graphics:../Images/HarvestingModelMod_gr_109.gif].

[Graphics:../Images/HarvestingModelMod_gr_110.gif]

[Graphics:../Images/HarvestingModelMod_gr_111.gif]

The solution functions corresponding to the above list of constants is:

[Graphics:../Images/HarvestingModelMod_gr_112.gif]

[Graphics:../Images/HarvestingModelMod_gr_113.gif]

Make them look nicer.  

[Graphics:../Images/HarvestingModelMod_gr_114.gif]

[Graphics:../Images/HarvestingModelMod_gr_115.gif]

Plot these functions, since a "table of functions" is being sent to the plot subroutine, the command Evaluate is necessary.   

[Graphics:../Images/HarvestingModelMod_gr_116.gif]


[Graphics:../Images/HarvestingModelMod_gr_117.gif]

[Graphics:../Images/HarvestingModelMod_gr_118.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004