\[ 2 (a+x) y'(x)+(1-b) b y(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.130936 (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 = 0.213 (sec), leaf count = 37
\[\left \{y \left (x \right ) = \frac {\left (c_{1} \BesselI \left (b -\frac {1}{2}, \frac {a}{x}\right )+c_{2} \BesselK \left (b -\frac {1}{2}, \frac {a}{x}\right )\right ) {\mathrm e}^{\frac {a}{x}}}{\sqrt {x}}\right \}\]