Consider the system described by 0 -=[-2₁2 x(t) = -2 -3 x(t) where x(t)=(x₁ (1)x₂ (t))". (a) Compute the state transition matrix Þ(t). (b) Using the state transition matrix from (a) and for the initial conditions x₁(0)=1 and x₂(0)=-1, find the solution x(t) for t≥0.

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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5. P3.19 of Dorf and Bishop
Consider the system described by
1
0-[23]
-2 -3
x(t) =
x(t)
where_x(t)=(x₁(t)x₂ (t))ª .
(a) Compute the state transition matrix (t).
(b) Using the state transition matrix from (a) and for the initial
conditions x₁(0)=1 and x₂(0)=-1, find the solution x(t) for t≥0.
Transcribed Image Text:5. P3.19 of Dorf and Bishop Consider the system described by 1 0-[23] -2 -3 x(t) = x(t) where_x(t)=(x₁(t)x₂ (t))ª . (a) Compute the state transition matrix (t). (b) Using the state transition matrix from (a) and for the initial conditions x₁(0)=1 and x₂(0)=-1, find the solution x(t) for t≥0.
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