8.2.1.18 Differential Equations

Condition: solve the differential equation by the operator method: \ [\ begin {array} {l} x^{(4)}-x^{\ prime \ prime} = \ cos t, \ quad X (0) = 0, \ Quad x^{\ prime} (0) = 0, \\ X^{\ Prime \ Prime} (0) = 0, \ Quad X^{\ Prime \ Prime \ Prime} (0) = 0 \ End {Array} \]