4. (i)
$$p \frac { \mathrm {~d} x } { \mathrm {~d} t } + q x = r \quad \text { where } p , q \text { and } r \text { are constants }$$
Given that \(x = 0\) when \(t = 0\)
- find \(x\) in terms of \(t\)
- find the limiting value of \(x\) as \(t \rightarrow \infty\)
(ii)
$$\frac { \mathrm { d } y } { \mathrm {~d} \theta } + 2 y = \sin \theta$$
Given that \(y = 0\) when \(\theta = 0\), find \(y\) in terms of \(\theta\)