8.2.1.11 Differential equations

Problem: Solve the equation \[ \int_{0}^{t} \sin (t-\tau) x(\tau) d \tau=x^{\prime \prime}+x+2 \cos t-4 \] under the given initial conditions \( x(0)=0, x^{\prime}(0)=0 \) (with respect to the function \( x(t) \) ).