9 Find \(x\) in terms of \(t\) given that
$$4 \frac { \mathrm {~d} ^ { 2 } x } { \mathrm {~d} t ^ { 2 } } + 4 \frac { \mathrm {~d} x } { \mathrm {~d} t } + x = 6 \mathrm { e } ^ { - 2 t }$$
and that, when \(t = 0 , x = \frac { 5 } { 3 }\) and \(\frac { \mathrm { d } x } { \mathrm {~d} t } = \frac { 7 } { 6 }\).
State \(\lim _ { t \rightarrow \infty } x\).
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9 Find $x$ in terms of $t$ given that
$$4 \frac { \mathrm {~d} ^ { 2 } x } { \mathrm {~d} t ^ { 2 } } + 4 \frac { \mathrm {~d} x } { \mathrm {~d} t } + x = 6 \mathrm { e } ^ { - 2 t }$$
and that, when $t = 0 , x = \frac { 5 } { 3 }$ and $\frac { \mathrm { d } x } { \mathrm {~d} t } = \frac { 7 } { 6 }$.
State $\lim _ { t \rightarrow \infty } x$.
\hfill \mbox{\textit{CAIE FP1 2013 Q9}}