Use a Green's function to find an integral expression for the solution of the equation

$$\frac{d^{2} \theta}{d t^{2}}+4 \frac{d \theta}{d t}+29 \theta=f(t)$$

for $t \geqslant 0$ subject to the initial conditions

$$\theta(0)=0 \quad \text { and } \quad \frac{d \theta}{d t}(0)=0$$