\[ 2 (a+x) y'(x)-(b-1) b y(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.113262 (sec), leaf count = 74
\[\left \{\left \{y(x)\to (-2)^{1-b} c_1 a^{1-b} \left (\frac {1}{x}\right )^{1-b} \, _1F_1\left (1-b;2-2 b;\frac {2 a}{x}\right )+(-2)^b c_2 a^b \left (\frac {1}{x}\right )^b \, _1F_1\left (b;2 b;\frac {2 a}{x}\right )\right \}\right \}\] ✓ Maple : cpu = 0.509 (sec), leaf count = 37
\[ \left \{ y \left ( x \right ) ={{{\rm e}^{{\frac {a}{x}}}} \left ( {{\sl I}_{b-{\frac {1}{2}}}\left ({\frac {a}{x}}\right )}{\it \_C1}+{{\sl K}_{b-{\frac {1}{2}}}\left ({\frac {a}{x}}\right )}{\it \_C2} \right ) {\frac {1}{\sqrt {x}}}} \right \} \]