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\noindent Quiz 1

\noindent Math 226, Section 02

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\noindent 1. Write down the solution $y(t)$ of the differential
equation $y' + 2ty = e^t$ that satisfies the initial condition
$y(2) = 3$.  Your answer should have an unevaluated (and 
unevaluatable!) definite integral in it.  (7 points)
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\noindent 2. Consider the differential equation 
$$
y'\left(1+\frac{t}{y}\right) =  \frac{\sin yt}{y}.
$$   
A theorem from class guarantees that this equation has unique solutions
$y(t)$ satisfying three of the following four initial conditions:
$y(1) = 1$, $y(0) = 2$, $y(-3) = 3$, and $y(\pi) = 1$.  For which of 
these conditions does the theorem {\it fail} to guarantee a unique
solution?  Why? (3 points)

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