8.2.2.7 Systems of Differential Equations

Condition: Find a solution to the problem of Koshi for the system of differential equations by exclusion and the operational method. \ [\ left \ {\ begin {array} {c} x^{\ prime} = 3 x+2 y \\ y^{\ prime \ prime} =-10 X-y \ End {Array} \ Right. \] \ [x = x (t), y = y (t), x (0) =-1, \ quad y (0) = 7 \ text {. } \]