\[ \boxed { \left ( {x}^{2}y \left ( x \right ) -1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -x \left ( y \left ( x \right ) \right ) ^{2}+1=0} \]
Mathematica: cpu = 7.835995 (sec), leaf count = 819 \[ \left \{\left \{y(x)\to \frac {6 x c_1-x}{6 c_1-1}+\frac {\sqrt [3]{-1944 c_1^2 x^3+648 c_1 x^3-54 x^3+1944 c_1^2-648 c_1+\sqrt {4 \left (54 x^2 c_1-9 x^2\right ){}^3+\left (-1944 c_1^2 x^3+648 c_1 x^3-54 x^3+1944 c_1^2-648 c_1+54\right ){}^2}+54}}{3 \sqrt [3]{2} \left (6 c_1-1\right )}-\frac {\sqrt [3]{2} \left (54 x^2 c_1-9 x^2\right )}{3 \left (6 c_1-1\right ) \sqrt [3]{-1944 c_1^2 x^3+648 c_1 x^3-54 x^3+1944 c_1^2-648 c_1+\sqrt {4 \left (54 x^2 c_1-9 x^2\right ){}^3+\left (-1944 c_1^2 x^3+648 c_1 x^3-54 x^3+1944 c_1^2-648 c_1+54\right ){}^2}+54}}\right \},\left \{y(x)\to \frac {6 x c_1-x}{6 c_1-1}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-1944 c_1^2 x^3+648 c_1 x^3-54 x^3+1944 c_1^2-648 c_1+\sqrt {4 \left (54 x^2 c_1-9 x^2\right ){}^3+\left (-1944 c_1^2 x^3+648 c_1 x^3-54 x^3+1944 c_1^2-648 c_1+54\right ){}^2}+54}}{6 \sqrt [3]{2} \left (6 c_1-1\right )}+\frac {\left (1+i \sqrt {3}\right ) \left (54 x^2 c_1-9 x^2\right )}{3\ 2^{2/3} \left (6 c_1-1\right ) \sqrt [3]{-1944 c_1^2 x^3+648 c_1 x^3-54 x^3+1944 c_1^2-648 c_1+\sqrt {4 \left (54 x^2 c_1-9 x^2\right ){}^3+\left (-1944 c_1^2 x^3+648 c_1 x^3-54 x^3+1944 c_1^2-648 c_1+54\right ){}^2}+54}}\right \},\left \{y(x)\to \frac {6 x c_1-x}{6 c_1-1}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-1944 c_1^2 x^3+648 c_1 x^3-54 x^3+1944 c_1^2-648 c_1+\sqrt {4 \left (54 x^2 c_1-9 x^2\right ){}^3+\left (-1944 c_1^2 x^3+648 c_1 x^3-54 x^3+1944 c_1^2-648 c_1+54\right ){}^2}+54}}{6 \sqrt [3]{2} \left (6 c_1-1\right )}+\frac {\left (1-i \sqrt {3}\right ) \left (54 x^2 c_1-9 x^2\right )}{3\ 2^{2/3} \left (6 c_1-1\right ) \sqrt [3]{-1944 c_1^2 x^3+648 c_1 x^3-54 x^3+1944 c_1^2-648 c_1+\sqrt {4 \left (54 x^2 c_1-9 x^2\right ){}^3+\left (-1944 c_1^2 x^3+648 c_1 x^3-54 x^3+1944 c_1^2-648 c_1+54\right ){}^2}+54}}\right \}\right \} \]
Maple: cpu = 0.562 (sec), leaf count = 1623 \[ \left \{ y \left ( x \right ) =-{\frac {1}{4\,{x}^{2}} \left ( 63\,{x}^{3 }-63\,{\frac {{x}^{2}}{{\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 }\sqrt [3]{{\it \_C1}\, \left ( -1+4\,\sqrt {-{\frac {5\,{x}^{6}-10\,{x }^{3}+5}{{\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2}}} -63\,{{\it \_C1}\,{x}^{4}{\frac {1}{\sqrt [3]{{\it \_C1}\, \left ( -1+4 \,\sqrt {-{\frac {5\,{x}^{6}-10\,{x}^{3}+5}{{\it \_C1}\,{x}^{6}-80\,{x }^{6}+160\,{x}^{3}-80}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{ 6}+160\,{x}^{3}-80 \right ) ^{2}}}}} \right ) \left ( {\frac {63\,{x}^{2 }}{4\,{\it \_C1}\,{x}^{6}-320\,{x}^{6}+640\,{x}^{3}-320}\sqrt [3]{{ \it \_C1}\, \left ( -1+4\,\sqrt {-{\frac {5\,{x}^{6}-10\,{x}^{3}+5}{{ \it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80}}} \right ) \left ( { \it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2}}}+{\frac { 63\,{\it \_C1}\,{x}^{4}}{4}{\frac {1}{\sqrt [3]{{\it \_C1}\, \left ( -1 +4\,\sqrt {-{\frac {5\,{x}^{6}-10\,{x}^{3}+5}{{\it \_C1}\,{x}^{6}-80\, {x}^{6}+160\,{x}^{3}-80}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x} ^{6}+160\,{x}^{3}-80 \right ) ^{2}}}}}-{\frac {63}{4}} \right ) ^{-1}},y \left ( x \right ) =-{\frac {1}{4\,{x}^{2}} \left ( 63\,{x}^{3}+{\frac { 63\,{x}^{2}}{2\,{\it \_C1}\,{x}^{6}-160\,{x}^{6}+320\,{x}^{3}-160} \sqrt [3]{{\it \_C1}\, \left ( -1+4\,\sqrt {-{\frac {5\,{x}^{6}-10\,{x} ^{3}+5}{{\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2}}} +{\frac {63\,{\it \_C1}\,{x}^{4}}{2}{\frac {1}{\sqrt [3]{{\it \_C1}\, \left ( -1+4\,\sqrt {-{\frac {5\,{x}^{6}-10\,{x}^{3}+5}{{\it \_C1}\,{x }^{6}-80\,{x}^{6}+160\,{x}^{3}-80}}} \right ) \left ( {\it \_C1}\,{x}^{ 6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2}}}}}-2\,i\sqrt {3} \left ( { \frac {63\,{x}^{2}}{4\,{\it \_C1}\,{x}^{6}-320\,{x}^{6}+640\,{x}^{3}- 320}\sqrt [3]{{\it \_C1}\, \left ( -1+4\,\sqrt {-{\frac {5\,{x}^{6}-10 \,{x}^{3}+5}{{\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2}}}-{\frac {63\,{\it \_C1}\,{x}^{4}}{4}{\frac {1}{\sqrt [3 ]{{\it \_C1}\, \left ( -1+4\,\sqrt {-{\frac {5\,{x}^{6}-10\,{x}^{3}+5}{ {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80}}} \right ) \left ( { \it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2}}}}} \right ) \right ) \left ( -{\frac {63\,{x}^{2}}{8\,{\it \_C1}\,{x}^{6} -640\,{x}^{6}+1280\,{x}^{3}-640}\sqrt [3]{{\it \_C1}\, \left ( -1+4\, \sqrt {-{\frac {5\,{x}^{6}-10\,{x}^{3}+5}{{\it \_C1}\,{x}^{6}-80\,{x}^ {6}+160\,{x}^{3}-80}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{6} +160\,{x}^{3}-80 \right ) ^{2}}}-{\frac {63\,{\it \_C1}\,{x}^{4}}{8}{ \frac {1}{\sqrt [3]{{\it \_C1}\, \left ( -1+4\,\sqrt {-{\frac {5\,{x}^{ 6}-10\,{x}^{3}+5}{{\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2}}}}}-{\frac {63}{4}}+{\frac {i}{2}}\sqrt {3} \left ( { \frac {63\,{x}^{2}}{4\,{\it \_C1}\,{x}^{6}-320\,{x}^{6}+640\,{x}^{3}- 320}\sqrt [3]{{\it \_C1}\, \left ( -1+4\,\sqrt {-{\frac {5\,{x}^{6}-10 \,{x}^{3}+5}{{\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2}}}-{\frac {63\,{\it \_C1}\,{x}^{4}}{4}{\frac {1}{\sqrt [3 ]{{\it \_C1}\, \left ( -1+4\,\sqrt {-{\frac {5\,{x}^{6}-10\,{x}^{3}+5}{ {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80}}} \right ) \left ( { \it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2}}}}} \right ) \right ) ^{-1}},y \left ( x \right ) =-{\frac {1}{4\,{x}^{2}} \left ( 63\,{x}^{3}+{\frac {63\,{x}^{2}}{2\,{\it \_C1}\,{x}^{6}-160\,{ x}^{6}+320\,{x}^{3}-160}\sqrt [3]{{\it \_C1}\, \left ( -1+4\,\sqrt {-{ \frac {5\,{x}^{6}-10\,{x}^{3}+5}{{\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\, {x}^{3}-80}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x} ^{3}-80 \right ) ^{2}}}+{\frac {63\,{\it \_C1}\,{x}^{4}}{2}{\frac {1}{ \sqrt [3]{{\it \_C1}\, \left ( -1+4\,\sqrt {-{\frac {5\,{x}^{6}-10\,{x} ^{3}+5}{{\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2}}} }}+2\,i\sqrt {3} \left ( {\frac {63\,{x}^{2}}{4\,{\it \_C1}\,{x}^{6}- 320\,{x}^{6}+640\,{x}^{3}-320}\sqrt [3]{{\it \_C1}\, \left ( -1+4\, \sqrt {-{\frac {5\,{x}^{6}-10\,{x}^{3}+5}{{\it \_C1}\,{x}^{6}-80\,{x}^ {6}+160\,{x}^{3}-80}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{6} +160\,{x}^{3}-80 \right ) ^{2}}}-{\frac {63\,{\it \_C1}\,{x}^{4}}{4}{ \frac {1}{\sqrt [3]{{\it \_C1}\, \left ( -1+4\,\sqrt {-{\frac {5\,{x}^{ 6}-10\,{x}^{3}+5}{{\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2}}}}} \right ) \right ) \left ( -{\frac {63\,{x}^{2}}{8\,{ \it \_C1}\,{x}^{6}-640\,{x}^{6}+1280\,{x}^{3}-640}\sqrt [3]{{\it \_C1} \, \left ( -1+4\,\sqrt {-{\frac {5\,{x}^{6}-10\,{x}^{3}+5}{{\it \_C1}\, {x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80}}} \right ) \left ( {\it \_C1}\,{x} ^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2}}}-{\frac {63\,{\it \_C1} \,{x}^{4}}{8}{\frac {1}{\sqrt [3]{{\it \_C1}\, \left ( -1+4\,\sqrt {-{ \frac {5\,{x}^{6}-10\,{x}^{3}+5}{{\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\, {x}^{3}-80}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x} ^{3}-80 \right ) ^{2}}}}}-{\frac {63}{4}}-{\frac {i}{2}}\sqrt {3} \left ( {\frac {63\,{x}^{2}}{4\,{\it \_C1}\,{x}^{6}-320\,{x}^{6}+640\, {x}^{3}-320}\sqrt [3]{{\it \_C1}\, \left ( -1+4\,\sqrt {-{\frac {5\,{x} ^{6}-10\,{x}^{3}+5}{{\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2}}}-{\frac {63\,{\it \_C1}\,{x}^{4}}{4}{\frac {1}{\sqrt [3 ]{{\it \_C1}\, \left ( -1+4\,\sqrt {-{\frac {5\,{x}^{6}-10\,{x}^{3}+5}{ {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80}}} \right ) \left ( { \it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2}}}}} \right ) \right ) ^{-1}} \right \} \]