8.2.2.11 Systems of Differential Equations

Condition: Solve the system of differential equations with the operator method: \ [\ left \ {\ begin {array} {l} x^{\ prime}+x = y+e^{t} \\ y^{\ prime}+y = x+e^^^^{t} \ end {Array} \ Quad X (0) = Y (0) = 1 \ Right. \]