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Differential Equations - Systems of Equations (Elimination Method)

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Solve the system of differential equations:
x''(t) + y'(t) - x(t) + y(t) = -1
x'(t) + y'(t) - x(t) = t^2
x''(t) + y'(t) - x(t) + y(t) = -1
x'(t) + y'(t) - x(t) = t^2
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