Question: Verify that the vector X is a solution of the given coupled system of the initial value problem. dx dy dt dt where X(0) =

Verify that the vector X is a solution of the given coupled system of the initial value problem.
$( begin{array}{c}frac{d x}{d t}-frac{d y}{d t}=x+y+2 e^{-t} frac{d x}{d t}-frac{d y}{d t}=x-y+3 x(0)=frac{1}{2},$

dx dy dt dt where X(0) = (3) e + (`)e ^ + ( dx dy dt dt I ( _ - _) MINMIN - = x+y+2e-t 5 x(0) = 1, y(0) = { for t 0 2 = x=y+3

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