(i) Find the particular solution of the differential equation

\(\frac{d^2x}{dt^2}+2\frac{dx}{dt}+10x=37\sin3t,\)

given that \(x=3\) and \(\dfrac{dx}{dt}=0\) when \(t=0\).

(ii) Show that, for large positive values of \(t\) and for any initial conditions,

\(x\approx\sqrt{37}\sin(3t-\phi),\)

where \(\phi\) is such that \(\tan\phi=6\).