Solve the ODE.

$x^{}+6x^{}+34x=5sin(6t),x(0)=x(0^{})=0$

$x(t)=e^{-3t}(\frac{9}{65}cos5t+\frac{6}{65}sin5t)-\frac{9}{65}cos6t-\frac{1}{130}sin6t$

$x(t)=e^{-3t}(\frac{9}{65}sin5t+\frac{6}{65}cos5t)-\frac{9}{65}cos6t-\frac{1}{130}sin6t$

$x(t)=e^{-3t}(\frac{9}{65}cos5t+\frac{6}{65}sin5t)-\frac{9}{65}sin6t-\frac{1}{130}sin6t$

$x(t)=e^{-3t}(\frac{9}{65}cos5t+\frac{6}{65}sin5t)-\frac{9}{65}cos6t-\frac{1}{130}cos6t$