- #1
stephen cripps
- 15
- 0
Homework Statement
The final part of the problem I am trying to solve requires the proof of the following equation:
[tex]\frac{d}{dr}(\frac{rf'(r)-f(r)+f^2(r)}{r^2 f^2(r)})=0[/tex][/B]
Homework Equations
I've been given the ansatz:
[tex]f(r)=(1-kr^2)^{-1}[/tex]
leading to
[tex]f'(r)=2krf^2(r)[/tex]
[tex]f''(r)=2kf^2(r)+8(kr)^2f^3(r)[/tex]
The Attempt at a Solution
Using the quotient rule on the first equation and cancelling some terms and the denominator gets me to:
[tex](rf)^2(rf''+2ff')-(rf'-f+f^2)(2rf^2+2r^2ff')=0[/tex]
Expanding, cancelling and subbing in for f' & f'' leads me to:
[tex]2kr^3f^4+8k^2r^5f^5+2rf^3-2rf^4-4kr^4f^3=0[/tex]
I have tried subbing in the ansatz value for f, but I still can't get the terms to cancel out. Would anybody be able to point out where I've made a mistake/ what I've missed?