# 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.