\[ \boxed { y \left ( x \right ) \left ( \left ( y \left ( x \right ) \right ) ^{2}+1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( 1-3\, \left ( y \left ( x \right ) \right ) ^{2} \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 0.521066 (sec), leaf count = 84 \[ \left \{\left \{y(x)\to -\frac {\sqrt {-2 c_1 x-2 c_2 c_1-1}}{\sqrt {2} \sqrt {c_1 x+c_2 c_1}}\right \},\left \{y(x)\to \frac {\sqrt {-2 c_1 x-2 c_2 c_1-1}}{\sqrt {2} \sqrt {c_1 x+c_2 c_1}}\right \}\right \} \]
Maple: cpu = 1.607 (sec), leaf count = 67 \[ \left \{ y \left ( x \right ) =-{\frac {1}{2\,{\it \_C1}\,x+2\,{\it \_C2 }}\sqrt {- \left ( 2\,{\it \_C1}\,x+2\,{\it \_C2} \right ) \left ( 2\,{ \it \_C1}\,x+2\,{\it \_C2}+1 \right ) }},y \left ( x \right ) ={\frac {1 }{2\,{\it \_C1}\,x+2\,{\it \_C2}}\sqrt {- \left ( 2\,{\it \_C1}\,x+2\,{ \it \_C2} \right ) \left ( 2\,{\it \_C1}\,x+2\,{\it \_C2}+1 \right ) }} \right \} \]