\[ -v (v+1) x y(x)+\left (2 x^2+1\right ) y'(x)+x \left (x^2+1\right ) y''(x)=0 \] ✓ Mathematica : cpu = 0.0990644 (sec), leaf count = 63
\[\left \{\left \{y(x)\to c_2 G_{2,2}^{2,0}\left (-x^2|\begin {array}{c} \frac {1-v}{2},\frac {v+2}{2} \\ 0,0 \\\end {array}\right )+c_1 \, _2F_1\left (\frac {v}{2}+\frac {1}{2},-\frac {v}{2};1;-x^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.849 (sec), leaf count = 52
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\mbox {$_2$F$_1$}(-{\frac {v}{2}},{\frac {1}{2}}+{\frac {v}{2}};\,{\frac {1}{2}};\,{x}^{2}+1)}+{\it \_C2}\,\sqrt {{x}^{2}+1}{\mbox {$_2$F$_1$}(1+{\frac {v}{2}},{\frac {1}{2}}-{\frac {v}{2}};\,{\frac {3}{2}};\,{x}^{2}+1)} \right \} \]