a$.$ Apply the Euler$-$Cauchy method to solve the differential equation $\frac{d}{dt}=-t,$ in the range $0(0\mathrm{.}1)0\mathrm{.}5,$ given the initial condition that at $t=0,=2$

$4$ Marks

b$.$ The current in an electric circuit is given by the equation $Ri+L\frac{di}{dt}=0,$ where $L$ and $R$ are constant. Show that $i=I{e}^{\frac{-Rt}{L}},$ given that $i=$I and $t=0$