\[ a+x y'(x)^2+y(x) y'(x)=0 \] ✓ Mathematica : cpu = 27.5637 (sec), leaf count = 11973
\[\left \{\left \{y(x)\to -\frac {1}{36} \sqrt {\frac {-1728 a^3 x^3-a^2 \sqrt {\frac {-2985984 a^6 x^6+\frac {41472 a^4 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+5184 a^3 \cosh \left (3 c_1\right ) x^3+5184 a^3 \sinh \left (3 c_1\right ) x^3+648 a^2 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^2+\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{a^4 x^4}} x^2-648 a^2 \sqrt {-\frac {128}{9} a^2 x^2-\frac {8 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right )}{81 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+\frac {2 \cosh \left (3 c_1\right )}{81 a x}+\frac {2 \sinh \left (3 c_1\right )}{81 a x}-\frac {\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}{648 a^2 x^2}+\frac {\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{209952 a^4 x^4}-\frac {\left (2592 a^3 x^3+\left (71663616 a^6 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-71663616 a^6 x^6\right ) \sinh \left (3 c_1\right )\right ) \left (\cosh \left (6 c_1\right )+\sinh \left (6 c_1\right )\right )}{209952 a^6 \sqrt {\frac {-2985984 a^6 x^6+\frac {41472 a^4 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+5184 a^3 \cosh \left (3 c_1\right ) x^3+5184 a^3 \sinh \left (3 c_1\right ) x^3+648 a^2 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^2+\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{a^4 x^4}} x^6}} x^2+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )}{a^2 x^2}}\right \},\left \{y(x)\to \frac {1}{36} \sqrt {\frac {-1728 a^3 x^3-a^2 \sqrt {\frac {-2985984 a^6 x^6+\frac {41472 a^4 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+5184 a^3 \cosh \left (3 c_1\right ) x^3+5184 a^3 \sinh \left (3 c_1\right ) x^3+648 a^2 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^2+\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{a^4 x^4}} x^2-648 a^2 \sqrt {-\frac {128}{9} a^2 x^2-\frac {8 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right )}{81 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+\frac {2 \cosh \left (3 c_1\right )}{81 a x}+\frac {2 \sinh \left (3 c_1\right )}{81 a x}-\frac {\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}{648 a^2 x^2}+\frac {\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{209952 a^4 x^4}-\frac {\left (2592 a^3 x^3+\left (71663616 a^6 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-71663616 a^6 x^6\right ) \sinh \left (3 c_1\right )\right ) \left (\cosh \left (6 c_1\right )+\sinh \left (6 c_1\right )\right )}{209952 a^6 \sqrt {\frac {-2985984 a^6 x^6+\frac {41472 a^4 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+5184 a^3 \cosh \left (3 c_1\right ) x^3+5184 a^3 \sinh \left (3 c_1\right ) x^3+648 a^2 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^2+\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{a^4 x^4}} x^6}} x^2+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )}{a^2 x^2}}\right \},\left \{y(x)\to -\frac {1}{36} \sqrt {\frac {-1728 a^3 x^3-a^2 \sqrt {\frac {-2985984 a^6 x^6+\frac {41472 a^4 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+5184 a^3 \cosh \left (3 c_1\right ) x^3+5184 a^3 \sinh \left (3 c_1\right ) x^3+648 a^2 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^2+\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{a^4 x^4}} x^2+648 a^2 \sqrt {-\frac {128}{9} a^2 x^2-\frac {8 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right )}{81 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+\frac {2 \cosh \left (3 c_1\right )}{81 a x}+\frac {2 \sinh \left (3 c_1\right )}{81 a x}-\frac {\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}{648 a^2 x^2}+\frac {\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{209952 a^4 x^4}-\frac {\left (2592 a^3 x^3+\left (71663616 a^6 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-71663616 a^6 x^6\right ) \sinh \left (3 c_1\right )\right ) \left (\cosh \left (6 c_1\right )+\sinh \left (6 c_1\right )\right )}{209952 a^6 \sqrt {\frac {-2985984 a^6 x^6+\frac {41472 a^4 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+5184 a^3 \cosh \left (3 c_1\right ) x^3+5184 a^3 \sinh \left (3 c_1\right ) x^3+648 a^2 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^2+\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{a^4 x^4}} x^6}} x^2+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )}{a^2 x^2}}\right \},\left \{y(x)\to \frac {1}{36} \sqrt {\frac {-1728 a^3 x^3-a^2 \sqrt {\frac {-2985984 a^6 x^6+\frac {41472 a^4 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+5184 a^3 \cosh \left (3 c_1\right ) x^3+5184 a^3 \sinh \left (3 c_1\right ) x^3+648 a^2 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^2+\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{a^4 x^4}} x^2+648 a^2 \sqrt {-\frac {128}{9} a^2 x^2-\frac {8 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right )}{81 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+\frac {2 \cosh \left (3 c_1\right )}{81 a x}+\frac {2 \sinh \left (3 c_1\right )}{81 a x}-\frac {\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}{648 a^2 x^2}+\frac {\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{209952 a^4 x^4}-\frac {\left (2592 a^3 x^3+\left (71663616 a^6 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-71663616 a^6 x^6\right ) \sinh \left (3 c_1\right )\right ) \left (\cosh \left (6 c_1\right )+\sinh \left (6 c_1\right )\right )}{209952 a^6 \sqrt {\frac {-2985984 a^6 x^6+\frac {41472 a^4 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+5184 a^3 \cosh \left (3 c_1\right ) x^3+5184 a^3 \sinh \left (3 c_1\right ) x^3+648 a^2 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^2+\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{a^4 x^4}} x^6}} x^2+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )}{a^2 x^2}}\right \},\left \{y(x)\to -\frac {1}{36} \sqrt {\frac {-1728 a^3 x^3+a^2 \sqrt {\frac {-2985984 a^6 x^6+\frac {41472 a^4 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+5184 a^3 \cosh \left (3 c_1\right ) x^3+5184 a^3 \sinh \left (3 c_1\right ) x^3+648 a^2 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^2+\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{a^4 x^4}} x^2-648 a^2 \sqrt {-\frac {128}{9} a^2 x^2-\frac {8 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right )}{81 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+\frac {2 \cosh \left (3 c_1\right )}{81 a x}+\frac {2 \sinh \left (3 c_1\right )}{81 a x}-\frac {\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}{648 a^2 x^2}+\frac {\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{209952 a^4 x^4}+\frac {\left (2592 a^3 x^3+\left (71663616 a^6 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-71663616 a^6 x^6\right ) \sinh \left (3 c_1\right )\right ) \left (\cosh \left (6 c_1\right )+\sinh \left (6 c_1\right )\right )}{209952 a^6 \sqrt {\frac {-2985984 a^6 x^6+\frac {41472 a^4 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+5184 a^3 \cosh \left (3 c_1\right ) x^3+5184 a^3 \sinh \left (3 c_1\right ) x^3+648 a^2 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^2+\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{a^4 x^4}} x^6}} x^2+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )}{a^2 x^2}}\right \},\left \{y(x)\to \frac {1}{36} \sqrt {\frac {-1728 a^3 x^3+a^2 \sqrt {\frac {-2985984 a^6 x^6+\frac {41472 a^4 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+5184 a^3 \cosh \left (3 c_1\right ) x^3+5184 a^3 \sinh \left (3 c_1\right ) x^3+648 a^2 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^2+\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{a^4 x^4}} x^2-648 a^2 \sqrt {-\frac {128}{9} a^2 x^2-\frac {8 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right )}{81 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+\frac {2 \cosh \left (3 c_1\right )}{81 a x}+\frac {2 \sinh \left (3 c_1\right )}{81 a x}-\frac {\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}{648 a^2 x^2}+\frac {\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{209952 a^4 x^4}+\frac {\left (2592 a^3 x^3+\left (71663616 a^6 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-71663616 a^6 x^6\right ) \sinh \left (3 c_1\right )\right ) \left (\cosh \left (6 c_1\right )+\sinh \left (6 c_1\right )\right )}{209952 a^6 \sqrt {\frac {-2985984 a^6 x^6+\frac {41472 a^4 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+5184 a^3 \cosh \left (3 c_1\right ) x^3+5184 a^3 \sinh \left (3 c_1\right ) x^3+648 a^2 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^2+\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{a^4 x^4}} x^6}} x^2+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )}{a^2 x^2}}\right \},\left \{y(x)\to -\frac {1}{36} \sqrt {\frac {-1728 a^3 x^3+a^2 \sqrt {\frac {-2985984 a^6 x^6+\frac {41472 a^4 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+5184 a^3 \cosh \left (3 c_1\right ) x^3+5184 a^3 \sinh \left (3 c_1\right ) x^3+648 a^2 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^2+\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{a^4 x^4}} x^2+648 a^2 \sqrt {-\frac {128}{9} a^2 x^2-\frac {8 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right )}{81 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+\frac {2 \cosh \left (3 c_1\right )}{81 a x}+\frac {2 \sinh \left (3 c_1\right )}{81 a x}-\frac {\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}{648 a^2 x^2}+\frac {\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{209952 a^4 x^4}+\frac {\left (2592 a^3 x^3+\left (71663616 a^6 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-71663616 a^6 x^6\right ) \sinh \left (3 c_1\right )\right ) \left (\cosh \left (6 c_1\right )+\sinh \left (6 c_1\right )\right )}{209952 a^6 \sqrt {\frac {-2985984 a^6 x^6+\frac {41472 a^4 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+5184 a^3 \cosh \left (3 c_1\right ) x^3+5184 a^3 \sinh \left (3 c_1\right ) x^3+648 a^2 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^2+\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{a^4 x^4}} x^6}} x^2+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )}{a^2 x^2}}\right \},\left \{y(x)\to \frac {1}{36} \sqrt {\frac {-1728 a^3 x^3+a^2 \sqrt {\frac {-2985984 a^6 x^6+\frac {41472 a^4 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+5184 a^3 \cosh \left (3 c_1\right ) x^3+5184 a^3 \sinh \left (3 c_1\right ) x^3+648 a^2 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^2+\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{a^4 x^4}} x^2+648 a^2 \sqrt {-\frac {128}{9} a^2 x^2-\frac {8 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right )}{81 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+\frac {2 \cosh \left (3 c_1\right )}{81 a x}+\frac {2 \sinh \left (3 c_1\right )}{81 a x}-\frac {\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}{648 a^2 x^2}+\frac {\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{209952 a^4 x^4}+\frac {\left (2592 a^3 x^3+\left (71663616 a^6 x^6+1\right ) \cosh \left (3 c_1\right )+\left (1-71663616 a^6 x^6\right ) \sinh \left (3 c_1\right )\right ) \left (\cosh \left (6 c_1\right )+\sinh \left (6 c_1\right )\right )}{209952 a^6 \sqrt {\frac {-2985984 a^6 x^6+\frac {41472 a^4 \left (4096 a^3 \cosh \left (3 c_1\right ) x^3+4096 a^3 \sinh \left (3 c_1\right ) x^3+5 \cosh \left (6 c_1\right )+5 \sinh \left (6 c_1\right )\right ) x^4}{\sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+5184 a^3 \cosh \left (3 c_1\right ) x^3+5184 a^3 \sinh \left (3 c_1\right ) x^3+648 a^2 \sqrt [3]{10485760 a^6 \cosh \left (6 c_1\right ) x^6+10485760 a^6 \sinh \left (6 c_1\right ) x^6+2560 a^3 \cosh \left (9 c_1\right ) x^3+2560 a^3 \sinh \left (9 c_1\right ) x^3+\cosh \left (12 c_1\right )+\sinh \left (12 c_1\right )+\sqrt {-\left (\left (4096 a^3 x^3+1\right ) \cosh \left (\frac {3 c_1}{2}\right )+\left (1-4096 a^3 x^3\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\left (1024 a^3 x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (1024 a^3 x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^2+\left (-1728 a^3 x^3+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}{a^4 x^4}} x^6}} x^2+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )}{a^2 x^2}}\right \}\right \}\]
✓ Maple : cpu = 0.04 (sec), leaf count = 146
\[ \left \{ -{{\it \_C1}\,{x}^{2} \left ( {\frac {1}{x} \left ( -y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-4\,ax} \right ) } \right ) ^{{\frac {3}{2}}} \left ( -y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-4\,ax} \right ) ^{-2}}+x+{\frac {4\,a{x}^{2}}{3} \left ( -y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-4\,ax} \right ) ^{-2}}=0,{{\it \_C1}\,{x}^{2} \left ( {\frac {1}{x} \left ( -2\,y \left ( x \right ) -2\,\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-4\,ax} \right ) } \right ) ^{{\frac {3}{2}}} \left ( y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-4\,ax} \right ) ^{-2}}+x+{\frac {4\,a{x}^{2}}{3} \left ( y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-4\,ax} \right ) ^{-2}}=0 \right \} \]