\[ \left (x^2 y(x)-1\right ) y'(x)-x y(x)^2+1=0 \] ✓ Mathematica : cpu = 14.742 (sec), leaf count = 738
\[\left \{\left \{y(x)\to \frac {\left (1-6 c_1\right ) x^2+\left (6 c_1-1\right ) x \sqrt [3]{-\left (1-6 c_1\right ){}^2 x^3+\sqrt {\left (6 c_1-1\right ){}^3 \left (6 c_1 x^6+\left (2-12 c_1\right ) x^3+6 c_1-1\right )}+36 c_1^2-12 c_1+1}+\left (-\left (1-6 c_1\right ){}^2 x^3+\sqrt {\left (6 c_1-1\right ){}^3 \left (6 c_1 x^6+\left (2-12 c_1\right ) x^3+6 c_1-1\right )}+36 c_1^2-12 c_1+1\right ){}^{2/3}}{\left (6 c_1-1\right ) \sqrt [3]{-\left (1-6 c_1\right ){}^2 x^3+\sqrt {\left (6 c_1-1\right ){}^3 \left (6 c_1 x^6+\left (2-12 c_1\right ) x^3+6 c_1-1\right )}+36 c_1^2-12 c_1+1}}\right \},\left \{y(x)\to \frac {\left (1+i \sqrt {3}\right ) \left (6 c_1-1\right ) x^2+2 \left (6 c_1-1\right ) x \sqrt [3]{-\left (1-6 c_1\right ){}^2 x^3+\sqrt {\left (6 c_1-1\right ){}^3 \left (6 c_1 x^6+\left (2-12 c_1\right ) x^3+6 c_1-1\right )}+36 c_1^2-12 c_1+1}+i \left (\sqrt {3}+i\right ) \left (-\left (1-6 c_1\right ){}^2 x^3+\sqrt {\left (6 c_1-1\right ){}^3 \left (6 c_1 x^6+\left (2-12 c_1\right ) x^3+6 c_1-1\right )}+36 c_1^2-12 c_1+1\right ){}^{2/3}}{2 \left (6 c_1-1\right ) \sqrt [3]{-\left (1-6 c_1\right ){}^2 x^3+\sqrt {\left (6 c_1-1\right ){}^3 \left (6 c_1 x^6+\left (2-12 c_1\right ) x^3+6 c_1-1\right )}+36 c_1^2-12 c_1+1}}\right \},\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) \left (6 c_1-1\right ) x^2+2 \left (6 c_1-1\right ) x \sqrt [3]{-\left (1-6 c_1\right ){}^2 x^3+\sqrt {\left (6 c_1-1\right ){}^3 \left (6 c_1 x^6+\left (2-12 c_1\right ) x^3+6 c_1-1\right )}+36 c_1^2-12 c_1+1}-i \left (\sqrt {3}-i\right ) \left (-\left (1-6 c_1\right ){}^2 x^3+\sqrt {\left (6 c_1-1\right ){}^3 \left (6 c_1 x^6+\left (2-12 c_1\right ) x^3+6 c_1-1\right )}+36 c_1^2-12 c_1+1\right ){}^{2/3}}{2 \left (6 c_1-1\right ) \sqrt [3]{-\left (1-6 c_1\right ){}^2 x^3+\sqrt {\left (6 c_1-1\right ){}^3 \left (6 c_1 x^6+\left (2-12 c_1\right ) x^3+6 c_1-1\right )}+36 c_1^2-12 c_1+1}}\right \}\right \}\]
✓ Maple : cpu = 0.873 (sec), leaf count = 1338
\[ \left \{ y \left ( x \right ) ={1 \left ( \left ( \left ( -{\it \_C1}+80 \right ) {x}^{7}-160\,{x}^{4}+80\,x \right ) \sqrt [3]{4}\sqrt [3]{ \left ( -80+ \left ( {\it \_C1}-80 \right ) {x}^{6}+160\,{x}^{3} \right ) ^{2}{\it \_C1}\, \left ( -{\frac {1}{4}}+\sqrt {{\frac {-5\,{x}^{6}+10\,{x}^{3}-5}{-80+ \left ( {\it \_C1}-80 \right ) {x}^{6}+160\,{x}^{3}}}} \right ) }+ \left ( {{\it \_C1}}^{2}-80\,{\it \_C1} \right ) {x}^{8}+160\,{\it \_C1}\,{x}^{5}-80\,{\it \_C1}\,{x}^{2}+ \left ( {\it \_C1}\, \left ( -1+4\,\sqrt {{\frac {-5\,{x}^{6}+10\,{x}^{3}-5}{-80+ \left ( {\it \_C1}-80 \right ) {x}^{6}+160\,{x}^{3}}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2} \right ) ^{{\frac {2}{3}}} \right ) \left ( \left ( 80+ \left ( -{\it \_C1}+80 \right ) {x}^{6}-160\,{x}^{3} \right ) \sqrt [3]{4}\sqrt [3]{ \left ( -80+ \left ( {\it \_C1}-80 \right ) {x}^{6}+160\,{x}^{3} \right ) ^{2}{\it \_C1}\, \left ( -{\frac {1}{4}}+\sqrt {{\frac {-5\,{x}^{6}+10\,{x}^{3}-5}{-80+ \left ( {\it \_C1}-80 \right ) {x}^{6}+160\,{x}^{3}}}} \right ) }+{x}^{2} \left ( \left ( {{\it \_C1}}^{2}-80\,{\it \_C1} \right ) {x}^{8}+160\,{\it \_C1}\,{x}^{5}-80\,{\it \_C1}\,{x}^{2}+ \left ( {\it \_C1}\, \left ( -1+4\,\sqrt {{\frac {-5\,{x}^{6}+10\,{x}^{3}-5}{-80+ \left ( {\it \_C1}-80 \right ) {x}^{6}+160\,{x}^{3}}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2} \right ) ^{{\frac {2}{3}}} \right ) \right ) ^{-1}},y \left ( x \right ) ={1 \left ( \left ( \left ( -2\,{\it \_C1}+160 \right ) {x}^{7}-320\,{x}^{4}+160\,x \right ) \sqrt [3]{4}\sqrt [3]{ \left ( -80+ \left ( {\it \_C1}-80 \right ) {x}^{6}+160\,{x}^{3} \right ) ^{2}{\it \_C1}\, \left ( -{\frac {1}{4}}+\sqrt {{\frac {-5\,{x}^{6}+10\,{x}^{3}-5}{-80+ \left ( {\it \_C1}-80 \right ) {x}^{6}+160\,{x}^{3}}}} \right ) }+ \left ( -i{\it \_C1}\, \left ( {\it \_C1}-80 \right ) {x}^{8}-160\,i{\it \_C1}\,{x}^{5}+80\,i{\it \_C1}\,{x}^{2}+i \left ( {\it \_C1}\, \left ( -1+4\,\sqrt {{\frac {-5\,{x}^{6}+10\,{x}^{3}-5}{-80+ \left ( {\it \_C1}-80 \right ) {x}^{6}+160\,{x}^{3}}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2} \right ) ^{{\frac {2}{3}}} \right ) \sqrt {3}+ \left ( -{{\it \_C1}}^{2}+80\,{\it \_C1} \right ) {x}^{8}-160\,{\it \_C1}\,{x}^{5}+80\,{\it \_C1}\,{x}^{2}- \left ( {\it \_C1}\, \left ( -1+4\,\sqrt {{\frac {-5\,{x}^{6}+10\,{x}^{3}-5}{-80+ \left ( {\it \_C1}-80 \right ) {x}^{6}+160\,{x}^{3}}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2} \right ) ^{{\frac {2}{3}}} \right ) \left ( \left ( 160+ \left ( -2\,{\it \_C1}+160 \right ) {x}^{6}-320\,{x}^{3} \right ) \sqrt [3]{4}\sqrt [3]{ \left ( -80+ \left ( {\it \_C1}-80 \right ) {x}^{6}+160\,{x}^{3} \right ) ^{2}{\it \_C1}\, \left ( -{\frac {1}{4}}+\sqrt {{\frac {-5\,{x}^{6}+10\,{x}^{3}-5}{-80+ \left ( {\it \_C1}-80 \right ) {x}^{6}+160\,{x}^{3}}}} \right ) }+ \left ( \left ( -i{\it \_C1}\, \left ( {\it \_C1}-80 \right ) {x}^{8}-160\,i{\it \_C1}\,{x}^{5}+80\,i{\it \_C1}\,{x}^{2}+i \left ( {\it \_C1}\, \left ( -1+4\,\sqrt {{\frac {-5\,{x}^{6}+10\,{x}^{3}-5}{-80+ \left ( {\it \_C1}-80 \right ) {x}^{6}+160\,{x}^{3}}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2} \right ) ^{{\frac {2}{3}}} \right ) \sqrt {3}+ \left ( -{{\it \_C1}}^{2}+80\,{\it \_C1} \right ) {x}^{8}-160\,{\it \_C1}\,{x}^{5}+80\,{\it \_C1}\,{x}^{2}- \left ( {\it \_C1}\, \left ( -1+4\,\sqrt {{\frac {-5\,{x}^{6}+10\,{x}^{3}-5}{-80+ \left ( {\it \_C1}-80 \right ) {x}^{6}+160\,{x}^{3}}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2} \right ) ^{{\frac {2}{3}}} \right ) {x}^{2} \right ) ^{-1}},y \left ( x \right ) ={1 \left ( \left ( \left ( 2\,{\it \_C1}-160 \right ) {x}^{7}+320\,{x}^{4}-160\,x \right ) \sqrt [3]{4}\sqrt [3]{ \left ( -80+ \left ( {\it \_C1}-80 \right ) {x}^{6}+160\,{x}^{3} \right ) ^{2}{\it \_C1}\, \left ( -{\frac {1}{4}}+\sqrt {{\frac {-5\,{x}^{6}+10\,{x}^{3}-5}{-80+ \left ( {\it \_C1}-80 \right ) {x}^{6}+160\,{x}^{3}}}} \right ) }+ \left ( -i{\it \_C1}\, \left ( {\it \_C1}-80 \right ) {x}^{8}-160\,i{\it \_C1}\,{x}^{5}+80\,i{\it \_C1}\,{x}^{2}+i \left ( {\it \_C1}\, \left ( -1+4\,\sqrt {{\frac {-5\,{x}^{6}+10\,{x}^{3}-5}{-80+ \left ( {\it \_C1}-80 \right ) {x}^{6}+160\,{x}^{3}}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2} \right ) ^{{\frac {2}{3}}} \right ) \sqrt {3}+ \left ( {{\it \_C1}}^{2}-80\,{\it \_C1} \right ) {x}^{8}+160\,{\it \_C1}\,{x}^{5}-80\,{\it \_C1}\,{x}^{2}+ \left ( {\it \_C1}\, \left ( -1+4\,\sqrt {{\frac {-5\,{x}^{6}+10\,{x}^{3}-5}{-80+ \left ( {\it \_C1}-80 \right ) {x}^{6}+160\,{x}^{3}}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2} \right ) ^{{\frac {2}{3}}} \right ) \left ( \left ( -160+ \left ( 2\,{\it \_C1}-160 \right ) {x}^{6}+320\,{x}^{3} \right ) \sqrt [3]{4}\sqrt [3]{ \left ( -80+ \left ( {\it \_C1}-80 \right ) {x}^{6}+160\,{x}^{3} \right ) ^{2}{\it \_C1}\, \left ( -{\frac {1}{4}}+\sqrt {{\frac {-5\,{x}^{6}+10\,{x}^{3}-5}{-80+ \left ( {\it \_C1}-80 \right ) {x}^{6}+160\,{x}^{3}}}} \right ) }+ \left ( \left ( -i{\it \_C1}\, \left ( {\it \_C1}-80 \right ) {x}^{8}-160\,i{\it \_C1}\,{x}^{5}+80\,i{\it \_C1}\,{x}^{2}+i \left ( {\it \_C1}\, \left ( -1+4\,\sqrt {{\frac {-5\,{x}^{6}+10\,{x}^{3}-5}{-80+ \left ( {\it \_C1}-80 \right ) {x}^{6}+160\,{x}^{3}}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2} \right ) ^{{\frac {2}{3}}} \right ) \sqrt {3}+ \left ( {{\it \_C1}}^{2}-80\,{\it \_C1} \right ) {x}^{8}+160\,{\it \_C1}\,{x}^{5}-80\,{\it \_C1}\,{x}^{2}+ \left ( {\it \_C1}\, \left ( -1+4\,\sqrt {{\frac {-5\,{x}^{6}+10\,{x}^{3}-5}{-80+ \left ( {\it \_C1}-80 \right ) {x}^{6}+160\,{x}^{3}}}} \right ) \left ( {\it \_C1}\,{x}^{6}-80\,{x}^{6}+160\,{x}^{3}-80 \right ) ^{2} \right ) ^{{\frac {2}{3}}} \right ) {x}^{2} \right ) ^{-1}} \right \} \]