The variables \(x\) and \(y\) are related by the differential equation
\(6 \frac{\mathrm{~d}^{2} x}{\mathrm{~d} t^{2}}+5 \frac{\mathrm{~d} x}{\mathrm{~d} t}+x=t^{2}+10 t+13\)
(a) Find the general solution for \(x\) in terms of \(t\).
(b) State an approximate solution for large positive values of \(t\).