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Systems of Differential Equations : Modeling a Battle between Two Armies

When one models a pair of conventional forces in combat, the following system arises
x1' -a -b x1 p
x2' = -c -d x2 + q

The unknown functions x1(t) and x2(t) represent the strengths of opposing forces at time t. The terms -ax1 and -dx2 represent operational loss rates and -cx1 and -bx2 represent combat loss rates. The constants p and q represent the rates at which reinforcements arrive. Let a=1, b=4, c=3, d=2, and p=q=5. Use the method of Variation of Parameters to determine which forces will win with the following initial values:

a) x1(0) = 20, x2(0) = 20

b) x1(0) = 21, x2(0) = 20

c) x1(0) = 20, x2(0) = 21

Note: You can do this by hand or using Maple


Solution Summary

A system of ODEs is used to model a battle between two armies. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.