\[ y''(x)=-\frac {y(x) \left (-\left (a^2-1\right ) x^2+2 (a+3) b x-b^2\right )}{4 x^2} \] ✓ Mathematica : cpu = 0.020784 (sec), leaf count = 110
DSolve[Derivative[2][y][x] == -1/4*((-b^2 + 2*(3 + a)*b*x - (-1 + a^2)*x^2)*y[x])/x^2,y[x],x]
\[\left \{\left \{y(x)\to c_1 M_{\frac {(a+3) b}{2 \sqrt {a^2-1}},\frac {\sqrt {b \left (b^2+1\right )}}{2 \sqrt {b}}}\left (\sqrt {a^2-1} x\right )+c_2 W_{\frac {(a+3) b}{2 \sqrt {a^2-1}},\frac {\sqrt {b \left (b^2+1\right )}}{2 \sqrt {b}}}\left (\sqrt {a^2-1} x\right )\right \}\right \}\] ✓ Maple : cpu = 0.234 (sec), leaf count = 73
dsolve(diff(diff(y(x),x),x) = -1/4*(-x^2*(a^2-1)+2*(a+3)*b*x-b^2)/x^2*y(x),y(x))
\[y \left (x \right ) = c_{1} \WhittakerM \left (\frac {b \left (a +3\right )}{2 \sqrt {a^{2}-1}}, \frac {\sqrt {b^{2}+1}}{2}, \sqrt {a^{2}-1}\, x \right )+c_{2} \WhittakerW \left (\frac {b \left (a +3\right )}{2 \sqrt {a^{2}-1}}, \frac {\sqrt {b^{2}+1}}{2}, \sqrt {a^{2}-1}\, x \right )\]