8.2.2.8 Systems of Differential Equations

Condition: to intervene the system of linear differential equations under given initial conditions: \ [\ Left \ {\ Begin {Array} {l} x^{\ Primee \ Prime} -x^{\ Prime}+Y^{\ Prime} = e^{-t}+\ cos t \\ x^{\ prime} -y^{\ prime} -y^{\ prime} = 2 E^{t}+\ sin t^{\ prime} \ end {array} \ right. \] \ [t = 0, \ quad x = 2, \ quad x^{\ prime} = 1, y = 0, \ quad y^{\ prime} = 1 \]