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Find the complete solution to the following system of ordinary differential equations by Eigenvalue-Eigenvector method x1'= x2 - x3 - t x2'= x1 + x2

Find the complete solution to the following system of ordinary differential equations by
Eigenvalue-Eigenvector method


x1'= x2 – x3 – t
x2'= x1 + x2 – t^2
x3'= x1 + x3 - 1 + t
with the initial conditions:
(a) t = 0: x1 = 1, x2 = -1, x3 = 0.
(b) t = 0: x1 = 1, x2 = 1, x3 = 1

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Given system of ODE can be written as x1
0 1 −1
x1
−t x2 = 1 1 0 x2 + −t2 x3
10 1
x3
−1 + t (1) Now let
y (t) = A(t)y (2) 0 1 −1 1 1 0 , And we want to calculate fundamental matrix ie...

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