ODE No. 624

1. Problem in Latex
2. Mathematica input
3. Maple input

\[ y'(x)=\frac {x^{5/3}}{x^{4/3}+y(x)} \] ✓ Mathematica : cpu = 49.308 (sec), leaf count = 9837

\[\left \{\left \{y(x)\to \frac {1}{\frac {1}{2} \sqrt {\frac {72 x^{40/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {72 \cosh \left (3 c_1\right ) x^8}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {72 \sinh \left (3 c_1\right ) x^8}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right )}+\frac {72 \cosh \left (6 c_1\right ) x^{8/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {72 \sinh \left (6 c_1\right ) x^{8/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}{3 \sqrt [3]{2}}-\frac {64 \sqrt [3]{2} \cosh \left (3 c_1\right )}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}-\frac {64 \sqrt [3]{2} \sinh \left (3 c_1\right )}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}}-\frac {1}{2} \sqrt {-\frac {72 x^{40/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {72 \left (\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ) x^8}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right )}-\frac {72 \left (\cosh \left (6 c_1\right )+\sinh \left (6 c_1\right )\right ) x^{8/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {2 \left (-72 x^{34/3}+72 \cosh \left (3 c_1\right ) x^6+72 \sinh \left (3 c_1\right ) x^6-72 \cosh \left (6 c_1\right ) x^{2/3}-72 \sinh \left (6 c_1\right ) x^{2/3}\right ) x^2}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {2 \left (64 x^{11}-64 \cosh \left (3 c_1\right ) x^{17/3}-64 \sinh \left (3 c_1\right ) x^{17/3}+64 \cosh \left (6 c_1\right ) \sqrt [3]{x}+64 \sinh \left (6 c_1\right ) \sqrt [3]{x}\right ) x}{\left (27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )\right ) \sqrt {\frac {72 x^{40/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {72 \cosh \left (3 c_1\right ) x^8}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {72 \sinh \left (3 c_1\right ) x^8}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right )}+\frac {72 \cosh \left (6 c_1\right ) x^{8/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {72 \sinh \left (6 c_1\right ) x^{8/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}{3 \sqrt [3]{2}}-\frac {64 \sqrt [3]{2} \cosh \left (3 c_1\right )}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}-\frac {64 \sqrt [3]{2} \sinh \left (3 c_1\right )}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}}}-\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}{3 \sqrt [3]{2}}+\frac {64 \sqrt [3]{2} \left (\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right )}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}}}-x^{4/3}\right \},\left \{y(x)\to \frac {1}{\frac {1}{2} \sqrt {\frac {72 x^{40/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {72 \cosh \left (3 c_1\right ) x^8}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {72 \sinh \left (3 c_1\right ) x^8}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right )}+\frac {72 \cosh \left (6 c_1\right ) x^{8/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {72 \sinh \left (6 c_1\right ) x^{8/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}{3 \sqrt [3]{2}}-\frac {64 \sqrt [3]{2} \cosh \left (3 c_1\right )}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}-\frac {64 \sqrt [3]{2} \sinh \left (3 c_1\right )}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}}+\frac {1}{2} \sqrt {-\frac {72 x^{40/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {72 \left (\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ) x^8}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right )}-\frac {72 \left (\cosh \left (6 c_1\right )+\sinh \left (6 c_1\right )\right ) x^{8/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {2 \left (-72 x^{34/3}+72 \cosh \left (3 c_1\right ) x^6+72 \sinh \left (3 c_1\right ) x^6-72 \cosh \left (6 c_1\right ) x^{2/3}-72 \sinh \left (6 c_1\right ) x^{2/3}\right ) x^2}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {2 \left (64 x^{11}-64 \cosh \left (3 c_1\right ) x^{17/3}-64 \sinh \left (3 c_1\right ) x^{17/3}+64 \cosh \left (6 c_1\right ) \sqrt [3]{x}+64 \sinh \left (6 c_1\right ) \sqrt [3]{x}\right ) x}{\left (27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )\right ) \sqrt {\frac {72 x^{40/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {72 \cosh \left (3 c_1\right ) x^8}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {72 \sinh \left (3 c_1\right ) x^8}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right )}+\frac {72 \cosh \left (6 c_1\right ) x^{8/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {72 \sinh \left (6 c_1\right ) x^{8/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}{3 \sqrt [3]{2}}-\frac {64 \sqrt [3]{2} \cosh \left (3 c_1\right )}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}-\frac {64 \sqrt [3]{2} \sinh \left (3 c_1\right )}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}}}-\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}{3 \sqrt [3]{2}}+\frac {64 \sqrt [3]{2} \left (\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right )}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}}}-x^{4/3}\right \},\left \{y(x)\to \frac {1}{-\frac {1}{2} \sqrt {\frac {72 x^{40/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {72 \cosh \left (3 c_1\right ) x^8}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {72 \sinh \left (3 c_1\right ) x^8}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right )}+\frac {72 \cosh \left (6 c_1\right ) x^{8/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {72 \sinh \left (6 c_1\right ) x^{8/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}{3 \sqrt [3]{2}}-\frac {64 \sqrt [3]{2} \cosh \left (3 c_1\right )}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}-\frac {64 \sqrt [3]{2} \sinh \left (3 c_1\right )}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}}-\frac {1}{2} \sqrt {-\frac {72 x^{40/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {72 \left (\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ) x^8}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right )}-\frac {72 \left (\cosh \left (6 c_1\right )+\sinh \left (6 c_1\right )\right ) x^{8/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {2 \left (-72 x^{34/3}+72 \cosh \left (3 c_1\right ) x^6+72 \sinh \left (3 c_1\right ) x^6-72 \cosh \left (6 c_1\right ) x^{2/3}-72 \sinh \left (6 c_1\right ) x^{2/3}\right ) x^2}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {2 \left (64 x^{11}-64 \cosh \left (3 c_1\right ) x^{17/3}-64 \sinh \left (3 c_1\right ) x^{17/3}+64 \cosh \left (6 c_1\right ) \sqrt [3]{x}+64 \sinh \left (6 c_1\right ) \sqrt [3]{x}\right ) x}{\left (27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )\right ) \sqrt {\frac {72 x^{40/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {72 \cosh \left (3 c_1\right ) x^8}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {72 \sinh \left (3 c_1\right ) x^8}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right )}+\frac {72 \cosh \left (6 c_1\right ) x^{8/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {72 \sinh \left (6 c_1\right ) x^{8/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}{3 \sqrt [3]{2}}-\frac {64 \sqrt [3]{2} \cosh \left (3 c_1\right )}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}-\frac {64 \sqrt [3]{2} \sinh \left (3 c_1\right )}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}}}-\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}{3 \sqrt [3]{2}}+\frac {64 \sqrt [3]{2} \left (\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right )}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}}}-x^{4/3}\right \},\left \{y(x)\to \frac {1}{\frac {1}{2} \sqrt {-\frac {72 x^{40/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {72 \left (\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ) x^8}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right )}-\frac {72 \left (\cosh \left (6 c_1\right )+\sinh \left (6 c_1\right )\right ) x^{8/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {2 \left (-72 x^{34/3}+72 \cosh \left (3 c_1\right ) x^6+72 \sinh \left (3 c_1\right ) x^6-72 \cosh \left (6 c_1\right ) x^{2/3}-72 \sinh \left (6 c_1\right ) x^{2/3}\right ) x^2}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {2 \left (64 x^{11}-64 \cosh \left (3 c_1\right ) x^{17/3}-64 \sinh \left (3 c_1\right ) x^{17/3}+64 \cosh \left (6 c_1\right ) \sqrt [3]{x}+64 \sinh \left (6 c_1\right ) \sqrt [3]{x}\right ) x}{\left (27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )\right ) \sqrt {\frac {72 x^{40/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {72 \cosh \left (3 c_1\right ) x^8}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {72 \sinh \left (3 c_1\right ) x^8}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right )}+\frac {72 \cosh \left (6 c_1\right ) x^{8/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {72 \sinh \left (6 c_1\right ) x^{8/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}{3 \sqrt [3]{2}}-\frac {64 \sqrt [3]{2} \cosh \left (3 c_1\right )}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}-\frac {64 \sqrt [3]{2} \sinh \left (3 c_1\right )}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}}}-\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}{3 \sqrt [3]{2}}+\frac {64 \sqrt [3]{2} \left (\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right )}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}}-\frac {1}{2} \sqrt {\frac {72 x^{40/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {72 \cosh \left (3 c_1\right ) x^8}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {72 \sinh \left (3 c_1\right ) x^8}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}-\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right )}+\frac {72 \cosh \left (6 c_1\right ) x^{8/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {72 \sinh \left (6 c_1\right ) x^{8/3}}{27 x^{16}+27 \cosh \left (9 c_1\right )+27 \sinh \left (9 c_1\right )}+\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}{3 \sqrt [3]{2}}-\frac {64 \sqrt [3]{2} \cosh \left (3 c_1\right )}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}-\frac {64 \sqrt [3]{2} \sinh \left (3 c_1\right )}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^4}+\frac {1048576 \sinh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}+\frac {1048576 \cosh \left (9 c_1\right )}{729 \left (x^{16/3}+\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ){}^6}}}}}}-x^{4/3}\right \}\right \}\] ✓ Maple : cpu = 1.451 (sec), leaf count = 46

\[ \left \{ y \left ( x \right ) ={\frac {1}{2} \left ( {\it RootOf} \left ( {{\it \_Z}}^{192}+12\,{x}^{4/3}{{\it \_Z}}^{176}+48\,{x}^{8/3}{{\it \_Z}}^{160}+64\,{x}^{4}{{\it \_Z}}^{144}-{\it \_C1} \right ) \right ) ^{16}}+{\frac {1}{2}{x}^{{\frac {4}{3}}}} \right \} \]