Factorising and integrating a differential

1. Apr 28, 2012

eddysd

Having a bit of trouble with this equation, I need to find V explicitly and this would obviously be done by factorising and integrating, but I can't seem to factorise it correctly. I have what I think is the correct answer but can't do the steps to get there. Any help would be greatly appreciated.

δ2V/δr2 + 1/r δV/δr - V/r = 0

which I think goes to:

V = C1r/2 + C2/r

C1 and C2 being constants of integration.

2. Apr 28, 2012

tiny-tim

hi eddysd!
no, i think that would be δ2V/δr2 + 1/r δV/δr - V/r2 = 0

3. Apr 28, 2012

eddysd

Yes sorry, typo, that is the correct equation! Do you think you could tell me how to get from that to the equation for V?

4. Apr 28, 2012

JJacquelin

Solutions involves Bessel functions.

5. Apr 28, 2012

andrien

substiution r=exp(y) will give you the required answer .To know why multiply the eqn by r^2 and see the second term and it does not involve bessel functions.

Last edited: Apr 28, 2012
6. Apr 28, 2012

JJacquelin

Now it is an homogeneous ODE.
So, use the classical method : Let V=r*W and rewite the ODE where W is the unknown function.