Solving a Particle's Spiral Orbit under Central Force

[Varnson]

Homework Statement

A particle moves under the action of a central force in a spiral orbit given by r=a*theta. Show that the force is f(r) = (-L^2/mr^3)*[1 + (a^2)/(r^2)]

Homework Equations

The Attempt at a Solution

I know how to do the problem, but I keep ending up with a factor of 2 for the a^2 term. Any pointers on how to fix this? Thanks for the help!

 

[Kurdt]

If you post exactly what you've done, people will have a better idea of what mistakes you may have made.

 

[Varnson]

Sorry for that... I used the equation d^2u/dtheta^2 + u = (-1/ml^2u^2)*f(u^-1). For the second derivative of u with respect to theta i got 2*a*theta^-3, which i re-wrote as 2*a^2*u^3. I plugged that result into the diff. equation, but was unable to 'get rid of' the factor of 2 for the a^2 term. Any pointers?