Solution to Differential Equation I'm looking for a solution to the following differential equation:
$$ y'' = \frac{c_1}{y} - \frac{c_2}{y^2} $$
where $c_1$ and $c_2$ are non-zero constants, and  y is always positive.
The resulting function should be periodic. Any help is appreciated.

$$y' y'' = \frac12 \frac{d}{dx} (y'^2) = c_1 \frac{y'}{y} - c_2 \frac{y'}{y^2} $$
Integrate both sides to get
$$\frac12 y'^2 = c_1 \log{y} + \frac{c_2}{y} + K_1$$
where $K_1$ is a constant of integration.  Now take the square root of both sides and integrate to get
$$\pm x+K_2 = \frac1{\sqrt{2}}\int \frac{dy}{\sqrt{K_1+c_1 \log{y}+c_2 y^{-1}}}$$
At this point, nothing further comes to mind.
