solve the given system of differential equations. (dx_1)/(dt)=2x_1-3x_2 (dx_2)/(dt)=x_1-2x_2

tabita57i 2021-02-13 Answered
solve the given system of differential equations.
dx1dt=2x13x2
dx2dt=x12x2
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Expert Answer

timbalemX
Answered 2021-02-14 Author has 108 answers
Step 1
Consider the following system of differential equations:
dx1dt=2x13x2...(1)
dx2dt=x12x2
Substitute x1=dx2dt+2x2 in the equation (1):
ddt(dx2dt+2x2)=2(dx2dt+2x2)3x2
d2x2dt2+2dx2dt=2dx2dt+4x23x2
d2x2dt2x2=0
Step 2
The auxiliary equation is m21=0.
The roots of auxiliary equation are 1,−1.
Hence, the solution of homogeneous equation is x2=Aet+Bet.
A and B are constants.
Substitute value of x2 in the equation x1=dx2dt+2x2:
x1=ddt(Aet+Bet+2(Aet+Bet)
=AetBet+2Aet+2Bet
=3Aet+Bet
Step 3
Hence, the solution is
x1=3Aet+Bet
x2=Aet+Bet.
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Jeffrey Jordon
Answered 2021-11-03 Author has 2047 answers

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