The problem states as follows. Let $f(z)$ be a meromorphic function on an open set $\Omega$. Consider a differential equation \begin{align} y''+f(z)y=0. \hspace{1cm}(1) \end{align} Show that every solution of $(1)$ has an analytic continuation along any path $\gamma$ on $\Omega$, such that $\gamma$ avoids the poles of $f(z)$.

  • $\begingroup$ What is the independent variable in your ODE? Is it $z$? $\endgroup$ – avs Aug 30 '16 at 3:09
  • $\begingroup$ Yes, it is. $f$ only depends on $z$. $\endgroup$ – user364833 Aug 30 '16 at 3:13
  • $\begingroup$ See the ODE section of Cartan's Elementary Theory of Analytic Functions. $\endgroup$ – avs Aug 30 '16 at 6:04

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