\[ y''(x)=-\frac {y(x) \left (-\left (a^2-1\right ) x^2+2 (a+3) b x-b^2\right )}{4 x^2} \] ✓ Mathematica : cpu = 0.0338597 (sec), leaf count = 110
\[\left \{\left \{y(x)\to c_1 M_{\frac {(a+3) b}{2 \sqrt {a^2-1}},\frac {\sqrt {b \left (b^2+1\right )}}{2 \sqrt {b}}}\left (\sqrt {a^2-1} x\right )+c_2 W_{\frac {(a+3) b}{2 \sqrt {a^2-1}},\frac {\sqrt {b \left (b^2+1\right )}}{2 \sqrt {b}}}\left (\sqrt {a^2-1} x\right )\right \}\right \}\]
✓ Maple : cpu = 0.262 (sec), leaf count = 73
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl M}_{{\frac {b \left ( a+3 \right ) }{2}{\frac {1}{\sqrt {{a}^{2}-1}}}},\,{\frac {1}{2}\sqrt {{b}^{2}+1}}}\left (\sqrt {{a}^{2}-1}x\right )}+{\it \_C2}\,{{\sl W}_{{\frac {b \left ( a+3 \right ) }{2}{\frac {1}{\sqrt {{a}^{2}-1}}}},\,{\frac {1}{2}\sqrt {{b}^{2}+1}}}\left (\sqrt {{a}^{2}-1}x\right )} \right \} \]