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**Aryth** Let $\displaystyle c > 0$. Show that the function $\displaystyle \phi(x) = (c^2 - x^2)^{-1}$ is a solution to the initial value problem $\displaystyle \frac{dy}{dx} = 2xy^2$, $\displaystyle y(0) = \frac{1}{c^2}$, on the interval $\displaystyle -c < x < c$. Note that this solution becomes unbounded as x approaches $\displaystyle \pm c$. Thus, the solution exists on the interval $\displaystyle (-\delta, \delta)$ with $\displaystyle \delta = c$, but not for larger $\displaystyle \delta$.