14 On an isolated island some rabbits have been accidently introduced. In order to eliminate them, conservationists have introduced some birds of prey.
At time \(t\) years \(( t \geq 0 )\) there are \(x\) rabbits and \(y\) birds of prey.
At time \(t = 0\) there are 1755 rabbits and 30 birds of prey.
When \(t > 0\) it is assumed that:

• the rabbits will reproduce at a rate of \(a \%\) per year
• each bird of prey will kill, on average, \(b\) rabbits per year
• the death rate of the birds of prey is \(c\) birds per year
• the number of birds of prey will increase at a rate of \(d \%\) of the rabbit population per year.

This system is represented by the coupled differential equations: $$\begin{aligned} & \frac { \mathrm { d } x } { \mathrm {~d} t } = 0.4 x - 13 y
& \frac { \mathrm {~d} y } { \mathrm {~d} t } = 0.01 x - 1.95 \end{aligned}$$ 14

1. State the value of \(a\), the value of \(b\), the value of \(c\) and the value of \(d\)
   [0pt] [2 marks]
   14
2. Solve the coupled differential equations to find both \(x\) and \(y\) in terms of \(t\)