Use the Laplace transform to solve the initial value problem. 2. 2x' – 3y + y' = 0; x' + y' = t; x(0) = y(0) = 0 3. x' + 2y' – y = 1; 2x' + y = 0; x(0) = y(0) = 0 4. x' + y' – x = cos(t);x' + 2y' = 0;...

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Extracted text: Use the Laplace transform to solve the initial value problem. 2. 2x' – 3y + y' = 0; x' + y' = t; x(0) = y(0) = 0 3. x' + 2y' – y = 1; 2x' + y = 0; x(0) = y(0) = 0 4. x' + y' – x = cos(t);x' + 2y' = 0; x(0) = y(0) = 0 5. 3x' – y = 2t;x' + y' – y = 0; x(0) = y(0) = 0