Consider the system of coupled second$-$order differential equations

u$00($t $+1)$uv $+$ v$0=$ cos t

v$00=$ u$0+$ uv

with initial conditions

u$(0)=2,$ u$0(0)=1,$ v$(0)=3,$ v$0(0)=1.$

Using MuPad,use the second$-$order Runge$-$Kutta method with h $=0\mathrm{.}2$ and a $=2=3,$ b $=1=3,==3=2,$ to find

u$,$ u$0,$ v and v$0$ at t $=0\mathrm{.}2.$