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(Solved): Solve the system of differential equations x1=4x15x2+3x3x2=0x1 ...

$Solve the system of differential equations \[ \begin{array}{l} \left\{\begin{array}{l} x_{1}^{\prime}=4 x_{1}-5 x_{2}+3 x_{3}$

Solve the system of differential equations

⎩ ⎨ ⎧ x_{1}^{'} = 4 x_{1} - 5 x_{2} + 3 x_{3} x_{2}^{'} = 0 x_{1} - 1 x_{2} + 3 x_{3} x_{3}^{'} = 0 x_{1} - 6 x_{2} + 8 x_{3} x_{1} (0) = - 7, x_{2} (0) = - 5 x_{3} (0) = - 8 x_{1} (t) = x_{2} (t) = x_{3} (t) =

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To solve the given system of differential equations, we can write it in matrix form as follows:

x?=Ax,
where

To find the solution, we need to diagonalize the matrix A. Let's find its eigenvalues and eigenvectors:

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