What is the equation for a body's trajectory in a central force field?

[neworder1]

Homework Statement

Show that in a central force field \vec{F}(\vec{r})=f(r)\frac{\vec{r}}{r} the equation for a body's trajectory in terms of u=\frac{1}{r} is given by:
\ddot{u}+u=-\frac{mf(\frac{1}{u})}{L^{2}u^{2}}

where m is the body's mass and L is the angular momentum

Homework Equations

The Attempt at a Solution

Transforming Newton's equations for \ddot{r} leads to ab equation for \ddot{u} and u where unfortunately \dot{u} also appears and I don't know how to eliminate it from the equation.

 

[malawi_glenn]

can you show us how you did it?

 

[azatkgz]

\ddot u=\frac{d^2u}{d\theta^2}