\[ 2 (a+x) y'(x)+(1-b) b y(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.1112 (sec), leaf count = 74
DSolve[(1 - b)*b*y[x] + 2*(a + x)*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to (-2)^{1-b} c_1 a^{1-b} \left (\frac {1}{x}\right )^{1-b} \, _1F_1\left (1-b;2-2 b;\frac {2 a}{x}\right )+(-2)^b c_2 a^b \left (\frac {1}{x}\right )^b \, _1F_1\left (b;2 b;\frac {2 a}{x}\right )\right \}\right \}\] ✓ Maple : cpu = 0.077 (sec), leaf count = 37
dsolve(x^2*diff(diff(y(x),x),x)+2*(x+a)*diff(y(x),x)-b*(b-1)*y(x)=0,y(x))
\[y \left (x \right ) = \frac {{\mathrm e}^{\frac {a}{x}} \left (\BesselK \left (b -\frac {1}{2}, \frac {a}{x}\right ) c_{2}+\BesselI \left (b -\frac {1}{2}, \frac {a}{x}\right ) c_{1}\right )}{\sqrt {x}}\]