Let $y(t)$ be the solution to $y^{}=5t{e}^{-y}$ satisfying $y(0)=1.$

$($a$)$ Use Euler's Method with time step $h=0\mathrm{.}2$ to approximate $y(0\mathrm{.}2),y(0\mathrm{.}4),$dots,$y(1\mathrm{.}0).$

$\backslash$table$[[k,t_k,y_k$