Example 14.   Solve the D. E.  [Graphics:Images/HarvestingModelMod_gr_254.gif]  using the formula with the initial condition  [Graphics:Images/HarvestingModelMod_gr_255.gif].  

Solution 14.

First, verify that the formula for the general solution is correct.

[Graphics:../Images/HarvestingModelMod_gr_256.gif]

[Graphics:../Images/HarvestingModelMod_gr_257.gif]

[Graphics:../Images/HarvestingModelMod_gr_258.gif]


[Graphics:../Images/HarvestingModelMod_gr_260.gif]

[Graphics:../Images/HarvestingModelMod_gr_261.gif]

[Graphics:../Images/HarvestingModelMod_gr_262.gif]

 

 

Aside.  You may need to identify the relationship between the arbitrary constants, i. e.  [Graphics:../Images/HarvestingModelMod_gr_263.gif].

First, verify that the formula for the solution with the initial condition  [Graphics:../Images/HarvestingModelMod_gr_264.gif]  is correct.

[Graphics:../Images/HarvestingModelMod_gr_265.gif]

[Graphics:../Images/HarvestingModelMod_gr_266.gif]

[Graphics:../Images/HarvestingModelMod_gr_267.gif]


[Graphics:../Images/HarvestingModelMod_gr_268.gif]


[Graphics:../Images/HarvestingModelMod_gr_269.gif]


[Graphics:../Images/HarvestingModelMod_gr_270.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004