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(Solved): homework 1) SOlVE the following system of differential equations: x=6x3y+8ety=y+2x+4etx(0) ...

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$1) SOlVE the following system of differential equations: \[ \begin{array}{l} \dot{x}=6 x-3 y+8 e^{t} \\ \dot{y}=y+2 x+4 e^{t}$

1) SOlVE the following system of differential equations:

\overset{x}{˙} = 6 x - 3 y + 8 e^{t} \overset{y}{˙} = y + 2 x + 4 e^{t} x (0) = - 1 y (0) = 0

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writing the given differential equations in the problem :

writing the system of equations in matrix form :

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