\[ x y'(x)^2+2 y(x) y'(x)-x=0 \] ✓ Mathematica : cpu = 1.72883 (sec), leaf count = 6977
\[\left \{\left \{y(x)\to \frac {-\sqrt {\frac {36 x^6+\frac {36\ 2^{2/3} \left (2 x^6-\cosh \left (6 c_1\right )-\sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}}}+9 \sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}} x^2+\cosh \left (6 c_1\right )+\sinh \left (6 c_1\right )}{x^4}} x^2-9 \sqrt {\frac {8 x^2}{9}-\frac {4\ 2^{2/3} \left (2 x^6-\cosh \left (6 c_1\right )-\sinh \left (6 c_1\right )\right )}{9 \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}}}-\frac {\sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}}}{9 x^2}+\frac {2 \cosh \left (6 c_1\right )}{81 x^4}+\frac {2 \sinh \left (6 c_1\right )}{81 x^4}-\frac {2 \left (-432 \cosh \left (3 c_1\right ) x^6-432 \sinh \left (3 c_1\right ) x^6+\cosh \left (9 c_1\right )+\sinh \left (9 c_1\right )\right )}{81 \sqrt {\frac {36 x^6+\frac {36\ 2^{2/3} \left (2 x^6-\cosh \left (6 c_1\right )-\sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}}}+9 \sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}} x^2+\cosh \left (6 c_1\right )+\sinh \left (6 c_1\right )}{x^4}} x^6}} x^2+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )}{18 x^2}\right \},\left \{y(x)\to \frac {-\sqrt {\frac {36 x^6+\frac {36\ 2^{2/3} \left (2 x^6-\cosh \left (6 c_1\right )-\sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}}}+9 \sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}} x^2+\cosh \left (6 c_1\right )+\sinh \left (6 c_1\right )}{x^4}} x^2+9 \sqrt {\frac {8 x^2}{9}-\frac {4\ 2^{2/3} \left (2 x^6-\cosh \left (6 c_1\right )-\sinh \left (6 c_1\right )\right )}{9 \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}}}-\frac {\sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}}}{9 x^2}+\frac {2 \cosh \left (6 c_1\right )}{81 x^4}+\frac {2 \sinh \left (6 c_1\right )}{81 x^4}-\frac {2 \left (-432 \cosh \left (3 c_1\right ) x^6-432 \sinh \left (3 c_1\right ) x^6+\cosh \left (9 c_1\right )+\sinh \left (9 c_1\right )\right )}{81 \sqrt {\frac {36 x^6+\frac {36\ 2^{2/3} \left (2 x^6-\cosh \left (6 c_1\right )-\sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}}}+9 \sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}} x^2+\cosh \left (6 c_1\right )+\sinh \left (6 c_1\right )}{x^4}} x^6}} x^2+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )}{18 x^2}\right \},\left \{y(x)\to \frac {\sqrt {\frac {36 x^6+\frac {36\ 2^{2/3} \left (2 x^6-\cosh \left (6 c_1\right )-\sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}}}+9 \sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}} x^2+\cosh \left (6 c_1\right )+\sinh \left (6 c_1\right )}{x^4}} x^2-9 \sqrt {\frac {8 x^2}{9}-\frac {4\ 2^{2/3} \left (2 x^6-\cosh \left (6 c_1\right )-\sinh \left (6 c_1\right )\right )}{9 \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}}}-\frac {\sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}}}{9 x^2}+\frac {2 \cosh \left (6 c_1\right )}{81 x^4}+\frac {2 \sinh \left (6 c_1\right )}{81 x^4}+\frac {2 \left (-432 \cosh \left (3 c_1\right ) x^6-432 \sinh \left (3 c_1\right ) x^6+\cosh \left (9 c_1\right )+\sinh \left (9 c_1\right )\right )}{81 \sqrt {\frac {36 x^6+\frac {36\ 2^{2/3} \left (2 x^6-\cosh \left (6 c_1\right )-\sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}}}+9 \sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}} x^2+\cosh \left (6 c_1\right )+\sinh \left (6 c_1\right )}{x^4}} x^6}} x^2+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )}{18 x^2}\right \},\left \{y(x)\to \frac {\sqrt {\frac {36 x^6+\frac {36\ 2^{2/3} \left (2 x^6-\cosh \left (6 c_1\right )-\sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}}}+9 \sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}} x^2+\cosh \left (6 c_1\right )+\sinh \left (6 c_1\right )}{x^4}} x^2+9 \sqrt {\frac {8 x^2}{9}-\frac {4\ 2^{2/3} \left (2 x^6-\cosh \left (6 c_1\right )-\sinh \left (6 c_1\right )\right )}{9 \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}}}-\frac {\sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}}}{9 x^2}+\frac {2 \cosh \left (6 c_1\right )}{81 x^4}+\frac {2 \sinh \left (6 c_1\right )}{81 x^4}+\frac {2 \left (-432 \cosh \left (3 c_1\right ) x^6-432 \sinh \left (3 c_1\right ) x^6+\cosh \left (9 c_1\right )+\sinh \left (9 c_1\right )\right )}{81 \sqrt {\frac {36 x^6+\frac {36\ 2^{2/3} \left (2 x^6-\cosh \left (6 c_1\right )-\sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}}}+9 \sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6+40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )-\sinh \left (12 c_1\right )+\sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-16 x^6\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (15 c_1\right )+\sinh \left (15 c_1\right )\right )}} x^2+\cosh \left (6 c_1\right )+\sinh \left (6 c_1\right )}{x^4}} x^6}} x^2+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )}{18 x^2}\right \},\left \{y(x)\to -\frac {\sqrt {\frac {36 x^6+\frac {36\ 2^{2/3} \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) \left (\left (2 x^6-1\right ) \cosh \left (3 c_1\right )+\left (2 x^6+1\right ) \sinh \left (3 c_1\right )\right ) x^4}{\sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}}}+9 \sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}} x^2+\cosh \left (6 c_1\right )-\sinh \left (6 c_1\right )}{x^4}} x^2+\sqrt {72 x^2+\frac {36\ 2^{2/3} \left (\sinh \left (3 c_1\right )-\cosh \left (3 c_1\right )\right ) \left (\left (2 x^6-1\right ) \cosh \left (3 c_1\right )+\left (2 x^6+1\right ) \sinh \left (3 c_1\right )\right )}{\sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}}}-\frac {9 \sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}}}{x^2}+\frac {2 \cosh \left (6 c_1\right )}{x^4}-\frac {2 \sinh \left (6 c_1\right )}{x^4}-\frac {2 \left (432 \cosh \left (3 c_1\right ) x^6-432 \sinh \left (3 c_1\right ) x^6-\cosh \left (9 c_1\right )+\sinh \left (9 c_1\right )\right )}{\sqrt {\frac {36 x^6+\frac {36\ 2^{2/3} \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) \left (\left (2 x^6-1\right ) \cosh \left (3 c_1\right )+\left (2 x^6+1\right ) \sinh \left (3 c_1\right )\right ) x^4}{\sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}}}+9 \sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}} x^2+\cosh \left (6 c_1\right )-\sinh \left (6 c_1\right )}{x^4}} x^6}} x^2+\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )}{18 x^2}\right \},\left \{y(x)\to \frac {-\sqrt {\frac {36 x^6+\frac {36\ 2^{2/3} \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) \left (\left (2 x^6-1\right ) \cosh \left (3 c_1\right )+\left (2 x^6+1\right ) \sinh \left (3 c_1\right )\right ) x^4}{\sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}}}+9 \sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}} x^2+\cosh \left (6 c_1\right )-\sinh \left (6 c_1\right )}{x^4}} x^2+\sqrt {72 x^2+\frac {36\ 2^{2/3} \left (\sinh \left (3 c_1\right )-\cosh \left (3 c_1\right )\right ) \left (\left (2 x^6-1\right ) \cosh \left (3 c_1\right )+\left (2 x^6+1\right ) \sinh \left (3 c_1\right )\right )}{\sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}}}-\frac {9 \sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}}}{x^2}+\frac {2 \cosh \left (6 c_1\right )}{x^4}-\frac {2 \sinh \left (6 c_1\right )}{x^4}-\frac {2 \left (432 \cosh \left (3 c_1\right ) x^6-432 \sinh \left (3 c_1\right ) x^6-\cosh \left (9 c_1\right )+\sinh \left (9 c_1\right )\right )}{\sqrt {\frac {36 x^6+\frac {36\ 2^{2/3} \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) \left (\left (2 x^6-1\right ) \cosh \left (3 c_1\right )+\left (2 x^6+1\right ) \sinh \left (3 c_1\right )\right ) x^4}{\sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}}}+9 \sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}} x^2+\cosh \left (6 c_1\right )-\sinh \left (6 c_1\right )}{x^4}} x^6}} x^2-\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )}{18 x^2}\right \},\left \{y(x)\to \frac {\sqrt {\frac {36 x^6+\frac {36\ 2^{2/3} \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) \left (\left (2 x^6-1\right ) \cosh \left (3 c_1\right )+\left (2 x^6+1\right ) \sinh \left (3 c_1\right )\right ) x^4}{\sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}}}+9 \sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}} x^2+\cosh \left (6 c_1\right )-\sinh \left (6 c_1\right )}{x^4}} x^2-\sqrt {72 x^2+\frac {36\ 2^{2/3} \left (\sinh \left (3 c_1\right )-\cosh \left (3 c_1\right )\right ) \left (\left (2 x^6-1\right ) \cosh \left (3 c_1\right )+\left (2 x^6+1\right ) \sinh \left (3 c_1\right )\right )}{\sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}}}-\frac {9 \sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}}}{x^2}+\frac {2 \cosh \left (6 c_1\right )}{x^4}-\frac {2 \sinh \left (6 c_1\right )}{x^4}+\frac {2 \left (432 \cosh \left (3 c_1\right ) x^6-432 \sinh \left (3 c_1\right ) x^6-\cosh \left (9 c_1\right )+\sinh \left (9 c_1\right )\right )}{\sqrt {\frac {36 x^6+\frac {36\ 2^{2/3} \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) \left (\left (2 x^6-1\right ) \cosh \left (3 c_1\right )+\left (2 x^6+1\right ) \sinh \left (3 c_1\right )\right ) x^4}{\sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}}}+9 \sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}} x^2+\cosh \left (6 c_1\right )-\sinh \left (6 c_1\right )}{x^4}} x^6}} x^2-\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )}{18 x^2}\right \},\left \{y(x)\to \frac {\sqrt {\frac {36 x^6+\frac {36\ 2^{2/3} \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) \left (\left (2 x^6-1\right ) \cosh \left (3 c_1\right )+\left (2 x^6+1\right ) \sinh \left (3 c_1\right )\right ) x^4}{\sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}}}+9 \sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}} x^2+\cosh \left (6 c_1\right )-\sinh \left (6 c_1\right )}{x^4}} x^2+\sqrt {72 x^2+\frac {36\ 2^{2/3} \left (\sinh \left (3 c_1\right )-\cosh \left (3 c_1\right )\right ) \left (\left (2 x^6-1\right ) \cosh \left (3 c_1\right )+\left (2 x^6+1\right ) \sinh \left (3 c_1\right )\right )}{\sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}}}-\frac {9 \sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}}}{x^2}+\frac {2 \cosh \left (6 c_1\right )}{x^4}-\frac {2 \sinh \left (6 c_1\right )}{x^4}+\frac {2 \left (432 \cosh \left (3 c_1\right ) x^6-432 \sinh \left (3 c_1\right ) x^6-\cosh \left (9 c_1\right )+\sinh \left (9 c_1\right )\right )}{\sqrt {\frac {36 x^6+\frac {36\ 2^{2/3} \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) \left (\left (2 x^6-1\right ) \cosh \left (3 c_1\right )+\left (2 x^6+1\right ) \sinh \left (3 c_1\right )\right ) x^4}{\sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}}}+9 \sqrt [3]{2} \sqrt [3]{32 x^{12}+40 \cosh \left (6 c_1\right ) x^6-40 \sinh \left (6 c_1\right ) x^6-\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\left (\cosh \left (18 c_1\right )-\sinh \left (18 c_1\right )\right ) \sqrt {\left (\left (16 x^6+1\right ) \cosh \left (3 c_1\right )+\left (16 x^6-1\right ) \sinh \left (3 c_1\right )\right ){}^3 \left (\cosh \left (21 c_1\right )+\sinh \left (21 c_1\right )\right )}} x^2+\cosh \left (6 c_1\right )-\sinh \left (6 c_1\right )}{x^4}} x^6}} x^2-\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )}{18 x^2}\right \}\right \}\]
✓ Maple : cpu = 0.075 (sec), leaf count = 109
\[ \left \{ x+{\frac {{\it \_C1}}{x} \left ( y \left ( x \right ) -\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}} \right ) \left ( {\frac {1}{{x}^{2}} \left ( 2\,{x}^{2}+6\, \left ( y \left ( x \right ) \right ) ^{2}-6\,y \left ( x \right ) \sqrt { \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}} \right ) } \right ) ^{-{\frac {2}{3}}}}=0,{\frac {{\it \_C1}}{x} \left ( \sqrt { \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}+y \left ( x \right ) \right ) \left ( {\frac {1}{{x}^{2}} \left ( 3\,y \left ( x \right ) \sqrt { \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}+{x}^{2}+3\, \left ( y \left ( x \right ) \right ) ^{2} \right ) } \right ) ^{-{\frac {2}{3}}}}+x=0 \right \} \]