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\noindent Quiz 7

\noindent Math 230

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\noindent 1. Let $y$ be the solution of the initial value problem
$$
y'' + xy' - y = 0, \quad y(0) = 1, \quad y'(0) = 0.
$$
Suppose that we represent $y$ as a power series 
$\sum_{n=0}^\infty c_n x^n$ centered at $0$.  
\begin{description}
\item[(a)] Find a recurrence relation for the coefficients $c_n$.
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\item[(b)] Write down the first three non-zero terms in the power series for 
$y$.
\end{description}

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