Use the Milne$-$Simpson predictor$-$corrector method $to$ approximate the solutions $to$ the initial$-$value

problems $in$ Exercise $4.$

$a.,y^{\text{'}}=\frac{2-2ty}{t^2+1},0t1,y(0)=1,$ with $h=0\mathrm{.}1$ actual solution $y(t)=\frac{2t+1}{t^2+1}.$

$b.,y^{\text{'}}=\frac{y^2}{1+t},1t2,y(1)=\frac{-1}{ln2},$ with $h=0\mathrm{.}1$ actual solution $y(t)=\frac{-1}{ln(t+1)}.$

$c.,y^{\text{'}}=\frac{y^2+y}{t},1t3,y(1)=-2,$ with $h=0\mathrm{.}2$ actual solution $y(t)=\frac{2t}{1-2t}.$

$d.,y^{\text{'}}=-ty+4\frac{t}{y},0t1,y(0)=1,$ with $h=0\mathrm{.}1$ actual solution $y(t)=\sqrt[\phantom{2}]{4-3e^{-t^2}}.$