Suppose that the gravitational force is not given by the inverse-square law, and instead is $$ F_{grav}=\left(\frac{A}{r^{2}}+\frac{B}{r^{4}}\right)\hat{r}, $$ where A and B are real constants. Derive the equations of motion and determine whether angular momentum is conserved. By using the substitution $r = 1/u$, transform the radial component of the equations of motion into a differential equation for $u$ as a function of the angular coordinate $\theta$. Determine for what values of $A$, $B$, and integration constants stationary solutions exist and whether they are stable.
I have found the differential equation for $U$, however I don't understand how one can determine the values of $A$, $B$ and the integration constants.
The differential equation is
$$ \frac{d^2u}{d^2\theta} + u = - A/h^2 - Bu^2/h^2 ,$$
where $A$, $B$ and $h$ are constants.
Any help is very much appreciated.
