\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +2\, \left ( x+a \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -b \left ( b-1 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.060508 (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 = 0.062 (sec), leaf count = 45 \[ \left \{ y \left ( x \right ) ={{\it \_C1}{{\rm e}^{{\frac {a}{x}}}}{ {\sl I}_{b-{\frac {1}{2}}}\left ({\frac {a}{x}}\right )}{\frac {1}{ \sqrt {x}}}}+{{\it \_C2}{{\rm e}^{{\frac {a}{x}}}}{{\sl K}_{b-{\frac { 1}{2}}}\left ({\frac {a}{x}}\right )}{\frac {1}{\sqrt {x}}}} \right \} \]