\[ \boxed { \left ( {x}^{2}+1 \right ) x{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) +3\, \left ( 2\,{x}^{2}+1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -12\,y \left ( x \right ) =0} \]
Mathematica: cpu = 0.241531 (sec), leaf count = 106 \[ \left \{\left \{y(x)\to \frac {1}{3} c_1 \left (2 x^2+1\right )+\frac {1}{3} c_2 x \sqrt {x^2+1}+\frac {c_3 \left (2 x^2+1\right ) \left (3 x^2+3 \sqrt {x^2+1} x^2 \log (x)-3 \sqrt {x^2+1} x^2 \log \left (\sqrt {x^2+1}+1\right )+1\right )}{6 \left (2 x^3+x\right )}\right \}\right \} \]
Maple: cpu = 0.374 (sec), leaf count = 56 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,x\sqrt {{x}^{2}+1}+{\frac {{ \it \_C2}}{x} \left ( 3\,{x}^{2}\sqrt {{x}^{2}+1}{\it Artanh} \left ( { \frac {1}{\sqrt {{x}^{2}+1}}} \right ) -3\,{x}^{2}-1 \right ) }+{\it \_C3}\, \left ( 2\,{x}^{2}+1 \right ) \right \} \]