Find the general solution for the nonhomogeneous first-order system. 5 0 -6 -BHM x' = 2 -1 -2 x + 0 4 -2 -4 9e2t 0 -t x(t) = 13C₁ +6C₂¹ + 5℃ze¯¹ + 6e²t

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A: Solution by using eigenvalues and eigenvectors as follows :

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A: Here is the solution of the given problem.

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A: Given system:

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A: Here we have to find the particular solution of given linear system with given initial conditions.

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A: Solution

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A: Hey, since there are multiple sub parts posted, we will answer first three sub parts. If you want…

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A: a)

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