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\textbf{Math 325: Differential Equations}
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\textbf{Quiz 2}\quad \textsl{February 2, 2001}
 
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You may  use your own calculator.
You may not use anything else.  You may not pass a calculator 
to another person.

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Show all your work.  Erase or cross out any work you do not want graded.

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Euler's method is used in Maple to evaluate the solution of
$$
y'= 2t+e^{-ty}, \qquad y(0)=1
$$
at  $t=.5\/$
using  step size  $h=.025\/$.
The calculation gives  $y_{19}=1.571690036\/$.

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a) Find $t_{19}\/$
and  $t_{20}\/$.


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b) What is the formula for  $y_{20}\/$?  (You do not need to give
it as a decimal, but your answer should involve only numbers and
simple operations on those numbers.)


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\textbf{Bonus} (3 points) Draw the picture which shows what you are
doing when you use Euler's method in a) and b).  Explain the picture
in words. 

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