a$)$ Define System Identification and briefly write on types of system identification $.$ b$)$ Briefly write on the followings:

i$)$ Auto Regressive Moving Average model $($ARMA$)$

ii$)$ Auto Regressive Integrated Moving Average model $($ARIMA$)$

a$)$ Briefly write on the $4^{th}$ order Runge$-$Kutta Method.

b$)$ Apply the fourth order Rung$-$Kutta method to solve

$\frac{dy}{dx}=x{y}^{\frac{1}{3}}$

$y(1)=1to$ obtain $y(1\mathrm{.}1)$