Example 18.   Solve the D. E.  [Graphics:Images/HarvestingModelMod_gr_305.gif]  using the formula with the initial condition  [Graphics:Images/HarvestingModelMod_gr_306.gif].  

Solution 18.

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

[Graphics:../Images/HarvestingModelMod_gr_307.gif]

[Graphics:../Images/HarvestingModelMod_gr_308.gif]

[Graphics:../Images/HarvestingModelMod_gr_309.gif]

[Graphics:../Images/HarvestingModelMod_gr_310.gif]

[Graphics:../Images/HarvestingModelMod_gr_311.gif]


[Graphics:../Images/HarvestingModelMod_gr_312.gif]

 

Aside.  You may need to identify the relationship between the arbitrary constants, i. e.  [Graphics:../Images/HarvestingModelMod_gr_313.gif].

[Graphics:../Images/HarvestingModelMod_gr_314.gif]

[Graphics:../Images/HarvestingModelMod_gr_315.gif]

First, verify that the formula for the solution with the initial condition  [Graphics:../Images/HarvestingModelMod_gr_316.gif]  is correct.

[Graphics:../Images/HarvestingModelMod_gr_317.gif]

[Graphics:../Images/HarvestingModelMod_gr_318.gif]

[Graphics:../Images/HarvestingModelMod_gr_319.gif]

[Graphics:../Images/HarvestingModelMod_gr_320.gif]

[Graphics:../Images/HarvestingModelMod_gr_321.gif]


[Graphics:../Images/HarvestingModelMod_gr_322.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004