Oklahoma State University

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Let $y(t)$ be the solution to $\frac{d y}{d t}=t e^{-y}$ satisfying $y(0)=0$.
(a) Use Euler's Method with time step $h=0.1$ to approximate $y(0.1), y(0.2), \ldots, y(0.5)$
(b) Use Separation of Variables to find $y(t)$ exactly.
(c) Compute the errors in the approximations to $y(0.1)$ and $y(0.5)$.