I'm reading the paper:

http://arxiv.org/abs/hep-ph/9907218

They have an ODE (eqn 7):

[tex]-\frac{1}{r^2}\frac{d}{d\phi}e^{-4kr\phi}\frac{dy_n}{d\phi}+m^2e^{-4kr\phi}y_n=m^2_ne^{-2kr\phi}y_n[/tex]

They then make a change of variables:

[tex]z_n=\frac{m_n}{k}e^{kr\phi}[/tex]

[tex]f_n=e^{-2kr\phi}y_n[/tex]

Then the ODE becomes:

[tex]z_n^2\frac{d^2f_n}{dz_n^2}+z_n\frac{df_n}{dz_n}+(z_n^2-[4+\frac{m^2}{k^2}])f_n=0[/tex]

My question is regarding this change of variables:

How do you 'know' how to change the variables so that the ODE comes out as this tiday Bessel function. Is this an

**art**almost, or is there some kind of technique??

Looking foward to gaining some insight here.

Richard