8.2.1.18 Differential equations

condition: Solve the differential equation using the operator method: \[ \begin{array}{l} x^{(4)}-x^{\prime \prime}=\cos t, \quad x(0)=0, \quad x^{\prime}(0)=0, \\ x^{\prime \prime}(0)=0, \quad x^{\prime \prime \prime}(0)=0 \end{array} \]