Use the Adams Variable Step$-$Size Predictor$-$Corrector Algorithm with TOL $=10-4$ to approximate the solutions to the following initial$-$value problems:

$($a$)$ y $=$ sint$+$e$\text{'},0<=1<=1,$ y$(0)=0,$ with hmax $=0\mathrm{.}2$ and hmin $=0\mathrm{.}01.$

$($b$)$ y$=-$ty$+4$t$/$y$,0<=$ t $<=1,$ y$(0)=1,$ with hmax $=0\mathrm{.}2$ and hmin $=0\mathrm{.}01.$