ODE No. 624

\[ y'(x)=\frac {x^{5/3}}{x^{4/3}+y(x)} \] ✓ Mathematica : cpu = 24.6633 (sec), leaf count = 9837

DSolve[Derivative[1][y][x] == x^(5/3)/(x^(4/3) + y[x]),y[x],x]
 

\[\left \{\left \{y(x)\to \frac {1}{\frac {1}{2} \sqrt {\frac {72 x^{40/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {72 \cosh (3 c_1) x^8}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {72 \sinh (3 c_1) x^8}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right )}+\frac {72 \cosh (6 c_1) x^{8/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {72 \sinh (6 c_1) x^{8/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}{3 \sqrt [3]{2}}-\frac {64 \sqrt [3]{2} \cosh (3 c_1)}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}-\frac {64 \sqrt [3]{2} \sinh (3 c_1)}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}}-\frac {1}{2} \sqrt {-\frac {72 x^{40/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {72 (\cosh (3 c_1)+\sinh (3 c_1)) x^8}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right )}-\frac {72 (\cosh (6 c_1)+\sinh (6 c_1)) x^{8/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {2 \left (-72 x^{34/3}+72 \cosh (3 c_1) x^6+72 \sinh (3 c_1) x^6-72 \cosh (6 c_1) x^{2/3}-72 \sinh (6 c_1) x^{2/3}\right ) x^2}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {2 \left (64 x^{11}-64 \cosh (3 c_1) x^{17/3}-64 \sinh (3 c_1) x^{17/3}+64 \cosh (6 c_1) \sqrt [3]{x}+64 \sinh (6 c_1) \sqrt [3]{x}\right ) x}{\left (27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)\right ) \sqrt {\frac {72 x^{40/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {72 \cosh (3 c_1) x^8}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {72 \sinh (3 c_1) x^8}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right )}+\frac {72 \cosh (6 c_1) x^{8/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {72 \sinh (6 c_1) x^{8/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}{3 \sqrt [3]{2}}-\frac {64 \sqrt [3]{2} \cosh (3 c_1)}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}-\frac {64 \sqrt [3]{2} \sinh (3 c_1)}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}}}-\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}{3 \sqrt [3]{2}}+\frac {64 \sqrt [3]{2} (\cosh (3 c_1)+\sinh (3 c_1))}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\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 (9 c_1)+27 \sinh (9 c_1)}-\frac {72 \cosh (3 c_1) x^8}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {72 \sinh (3 c_1) x^8}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right )}+\frac {72 \cosh (6 c_1) x^{8/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {72 \sinh (6 c_1) x^{8/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}{3 \sqrt [3]{2}}-\frac {64 \sqrt [3]{2} \cosh (3 c_1)}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}-\frac {64 \sqrt [3]{2} \sinh (3 c_1)}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}}+\frac {1}{2} \sqrt {-\frac {72 x^{40/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {72 (\cosh (3 c_1)+\sinh (3 c_1)) x^8}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right )}-\frac {72 (\cosh (6 c_1)+\sinh (6 c_1)) x^{8/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {2 \left (-72 x^{34/3}+72 \cosh (3 c_1) x^6+72 \sinh (3 c_1) x^6-72 \cosh (6 c_1) x^{2/3}-72 \sinh (6 c_1) x^{2/3}\right ) x^2}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {2 \left (64 x^{11}-64 \cosh (3 c_1) x^{17/3}-64 \sinh (3 c_1) x^{17/3}+64 \cosh (6 c_1) \sqrt [3]{x}+64 \sinh (6 c_1) \sqrt [3]{x}\right ) x}{\left (27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)\right ) \sqrt {\frac {72 x^{40/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {72 \cosh (3 c_1) x^8}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {72 \sinh (3 c_1) x^8}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right )}+\frac {72 \cosh (6 c_1) x^{8/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {72 \sinh (6 c_1) x^{8/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}{3 \sqrt [3]{2}}-\frac {64 \sqrt [3]{2} \cosh (3 c_1)}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}-\frac {64 \sqrt [3]{2} \sinh (3 c_1)}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}}}-\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}{3 \sqrt [3]{2}}+\frac {64 \sqrt [3]{2} (\cosh (3 c_1)+\sinh (3 c_1))}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\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 (9 c_1)+27 \sinh (9 c_1)}-\frac {72 \cosh (3 c_1) x^8}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {72 \sinh (3 c_1) x^8}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right )}+\frac {72 \cosh (6 c_1) x^{8/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {72 \sinh (6 c_1) x^{8/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}{3 \sqrt [3]{2}}-\frac {64 \sqrt [3]{2} \cosh (3 c_1)}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}-\frac {64 \sqrt [3]{2} \sinh (3 c_1)}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}}-\frac {1}{2} \sqrt {-\frac {72 x^{40/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {72 (\cosh (3 c_1)+\sinh (3 c_1)) x^8}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right )}-\frac {72 (\cosh (6 c_1)+\sinh (6 c_1)) x^{8/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {2 \left (-72 x^{34/3}+72 \cosh (3 c_1) x^6+72 \sinh (3 c_1) x^6-72 \cosh (6 c_1) x^{2/3}-72 \sinh (6 c_1) x^{2/3}\right ) x^2}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {2 \left (64 x^{11}-64 \cosh (3 c_1) x^{17/3}-64 \sinh (3 c_1) x^{17/3}+64 \cosh (6 c_1) \sqrt [3]{x}+64 \sinh (6 c_1) \sqrt [3]{x}\right ) x}{\left (27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)\right ) \sqrt {\frac {72 x^{40/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {72 \cosh (3 c_1) x^8}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {72 \sinh (3 c_1) x^8}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right )}+\frac {72 \cosh (6 c_1) x^{8/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {72 \sinh (6 c_1) x^{8/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}{3 \sqrt [3]{2}}-\frac {64 \sqrt [3]{2} \cosh (3 c_1)}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}-\frac {64 \sqrt [3]{2} \sinh (3 c_1)}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}}}-\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}{3 \sqrt [3]{2}}+\frac {64 \sqrt [3]{2} (\cosh (3 c_1)+\sinh (3 c_1))}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\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 (9 c_1)+27 \sinh (9 c_1)}+\frac {72 (\cosh (3 c_1)+\sinh (3 c_1)) x^8}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right )}-\frac {72 (\cosh (6 c_1)+\sinh (6 c_1)) x^{8/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {2 \left (-72 x^{34/3}+72 \cosh (3 c_1) x^6+72 \sinh (3 c_1) x^6-72 \cosh (6 c_1) x^{2/3}-72 \sinh (6 c_1) x^{2/3}\right ) x^2}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {2 \left (64 x^{11}-64 \cosh (3 c_1) x^{17/3}-64 \sinh (3 c_1) x^{17/3}+64 \cosh (6 c_1) \sqrt [3]{x}+64 \sinh (6 c_1) \sqrt [3]{x}\right ) x}{\left (27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)\right ) \sqrt {\frac {72 x^{40/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {72 \cosh (3 c_1) x^8}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {72 \sinh (3 c_1) x^8}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right )}+\frac {72 \cosh (6 c_1) x^{8/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {72 \sinh (6 c_1) x^{8/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}{3 \sqrt [3]{2}}-\frac {64 \sqrt [3]{2} \cosh (3 c_1)}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}-\frac {64 \sqrt [3]{2} \sinh (3 c_1)}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}}}-\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}{3 \sqrt [3]{2}}+\frac {64 \sqrt [3]{2} (\cosh (3 c_1)+\sinh (3 c_1))}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}}-\frac {1}{2} \sqrt {\frac {72 x^{40/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {72 \cosh (3 c_1) x^8}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {72 \sinh (3 c_1) x^8}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}-\frac {8 x^{8/3}}{9 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right )}+\frac {72 \cosh (6 c_1) x^{8/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {72 \sinh (6 c_1) x^{8/3}}{27 x^{16}+27 \cosh (9 c_1)+27 \sinh (9 c_1)}+\frac {\sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}{3 \sqrt [3]{2}}-\frac {64 \sqrt [3]{2} \cosh (3 c_1)}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}-\frac {64 \sqrt [3]{2} \sinh (3 c_1)}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2 \sqrt [3]{-\frac {1024 x^8}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^3}+\frac {1024 x^{8/3}}{27 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^2}+\sqrt {\frac {1048576 x^{16}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}-\frac {2097152 x^{32/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^5}+\frac {1048576 x^{16/3}}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^4}+\frac {1048576 \sinh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}+\frac {1048576 \cosh (9 c_1)}{729 \left (x^{16/3}+\cosh (3 c_1)+\sinh (3 c_1)\right ){}^6}}}}}}-x^{4/3}\right \}\right \}\] ✓ Maple : cpu = 29.544 (sec), leaf count = 46

dsolve(diff(y(x),x) = x^(5/3)/(y(x)+x^(4/3)),y(x))
 

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