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\textbf{Math 365: Honors Analysis I}
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\textbf{Quiz 1}\quad \textsl{September 10, 2000}

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1. Solve the initial value problem $y^2 y'' = y'$, $y(0) = 1$, $y'(0) = 1$.

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2. Suppose $\phi(x)$ is a solution to $y'' + e^xy' + x y = x$ whose graph
is tangent to the line $y = 1$ at some point. Prove that $\phi(x)$ is
constant.

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3. Find the general form of a particular solution to $y^{(4)} - y = e^x
+\sin(x)$. (Do not solve for the constants.)

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4. Use operator methods to find a particular solution to $y^{(100)} + y =
x^{200}$.

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