Let $y(t)$ be the solution to $\dot{y} = 3 t e^{-y}$ satisfying $y(0) = 1$.

(a) Use Euler's Method with time step $h = 0.2$ to approximate $y(0.2), \, y(0.4), ... , y(1.0)$.

(b) Use separation of variables to find $y(t)$ exactly.
$y(t)$ =

(c) Compute the error in the approximations to $y(0.2),\, y(0.6)$, and $y(1)$.
$\left|y(0.2)-y_1\right| =$

$\left|y(0.6)-y_3\right| =$

$\left|y(1)-y_{5}\right| =$