8.1.2.68 Second Order Differential Equations

Condition: find a general solution to the differential equation of the second order and a private solution that satisfies the specified initial conditions \ (\ left (x_ {0}, y_ {0}, y_ {0}^{\ prime} \ right) \). \ [y^{\ prime \ prime} -5 y^{\ prime} +6 y = 2 \ cos x, y_ {0} = 3, y_ {0} {\ prime} = \ frac {2}, x_ {0} = 0 \] = 0 \] = 0 \] = 0 \]