\[ \left (x^2 y(x)-1\right ) y'(x)-x y(x)^2+1=0 \] ✓ Mathematica : cpu = 15.1407 (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 = 0.805 (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 \} \]