2nd order differential equation I'm working on the following 2nd order ODE:
$$
x^2 y''+2(2x-1/b^2) y'+2(1-(a/b)^2)y=0,
$$
where $b\neq 0$. It's very similar to the equation for the generalized Bessel polynomials (see http://en.wikipedia.org/wiki/Bessel_polynomials ); There's a slight difference in the factor in front of $y$ though. Any advise on how to handle the beast? Thanks a lot.

Mathematica tells me that after multiplying by a (horrible) power it's hypergeometric:
$
y(x)=c_1 \left(\frac{1}{x}\right)^{\frac{3 b^2-b \sqrt{8
   a^2+b^2}}{2 b^2}} \, _1F_1\left(\frac{3}{2}-\frac{\sqrt{b^4+8 a^2 b^2}}{2
   b^2};1-\frac{\sqrt{b^4+8 a^2 b^2}}{b^2};-\frac{2}{b^2 x}\right)$
$
\quad +\quad c_2
    \left(\frac{1}{x}\right)^{\frac{b \sqrt{8 a^2+b^2}+3 b^2}{2
   b^2}} \, _1F_1\left(\frac{\sqrt{b^4+8 a^2 b^2}}{2
   b^2}+\frac{3}{2};\frac{\sqrt{b^4+8 a^2 b^2}}{b^2}+1;-\frac{2}{b^2
   x}\right)
$
Enjoy!
