Originally Posted by

**CallumJ** Hi I'm having trouble expanding the following equation for the axially symmetric biharmonic equation in polar co-ordinates.

$\displaystyle \left ( \frac{d^2}{dr^2} + \frac{d}{rdr} \right ) \left ( \frac{d^2\phi}{dr^2} + \frac{d\phi}{rdr} \right ) = 0 $

When I expanded it I got:

$\displaystyle \frac{d^4\phi}{dr^2} + \frac{2d\phi}{r^3dr} + \frac{d^3\phi}{rdr^3} + \frac{d^3\phi}{rdr^3} - \frac{d\phi}{r^3dr} + \frac{d^2\phi}{r^2dr^2}$

$\displaystyle = \frac{d^4\phi}{dr^2} + \frac{2d^3\phi}{rdr^3} + \frac{d^2\phi}{r^2dr^2} + \frac{d\phi}{r^3dr}$

But it should be:

$\displaystyle = \frac{d^4\phi}{dr^2} + \frac{2d^3\phi}{rdr^3} - \frac{d^2\phi}{r^2dr^2} + \frac{d\phi}{r^3dr}$

Any help would be much appreciated regards,

Callum