\[ \boxed { x \left ( {x}^{2}-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( {x}^{2}-1 \right ) \left ( y \left ( x \right ) \right ) ^{2}-{x}^{2}=0} \]
Mathematica: cpu = 0.123516 (sec), leaf count = 82 \[ \left \{\left \{y(x)\to \frac {x \left (\frac {2 c_1 \left (E\left (x^2\right )-K\left (x^2\right )\right )}{\pi x}-2 x G_{2,2}^{2,0}\left (x^2| \begin {array}{c} -\frac {1}{2},\frac {1}{2} \\ -1,0 \\ \end {array} \right )\right )}{G_{2,2}^{2,0}\left (x^2| \begin {array}{c} \frac {1}{2},\frac {3}{2} \\ 0,0 \\ \end {array} \right )+\frac {2 c_1 E\left (x^2\right )}{\pi }}\right \}\right \} \]
Maple: cpu = 0.078 (sec), leaf count = 45 \[ \left \{ y \left ( x \right ) =-{\frac {{\it EllipticK} \left ( x \right ) }{{\it \_C1}\,{\it EllipticCE} \left ( x \right ) -{\it \_C1}\, {\it EllipticCK} \left ( x \right ) +{\it EllipticE} \left ( x \right ) }} +{\frac {{\it \_C1}\,{\it EllipticCE} \left ( x \right ) +{\it EllipticE } \left ( x \right ) }{{\it \_C1}\,{\it EllipticCE} \left ( x \right ) -{ \it \_C1}\,{\it EllipticCK} \left ( x \right ) +{\it EllipticE} \left ( x \right ) }} \right \} \]