You are given the following inhomogeneous system of first-order differential equations for x(t) and y(t) in matrix form: x ̇ = 2x + y + 3 et , y ̇ = 4x − y  What is the long-term behaviour of this particular solution as t becomes large? Does the ratio y/x tend to a fixed number, and if so what number?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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You are given the following inhomogeneous system of first-order differential
equations for x(t) and y(t) in matrix form:

x ̇ = 2x + y + 3 et ,
y ̇ = 4x − y 

What is the long-term behaviour of this particular solution as t becomes large? Does the ratio y/x tend to a fixed number, and if so what number?

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