#### 2.385   ODE No. 385

$-2 x^2 y'(x)+y'(x)^2+2 x y(x)=0$ Mathematica : cpu = 0.682529 (sec), leaf count = 6217

$\left \{\left \{y(x)\to -x^3 \left (\frac {1}{2} \sqrt {\frac {2 \left (8 e^{6 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}}+\frac {1}{18} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}-\frac {e^{6 c_1}}{9 x^6}+\frac {4}{81}}-\frac {1}{2} \sqrt {-\frac {\frac {64}{729}+\frac {64 e^{6 c_1}}{27 x^6}}{4 \sqrt {\frac {2 \left (8 e^{6 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}}+\frac {1}{18} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}-\frac {e^{6 c_1}}{9 x^6}+\frac {4}{81}}}-\frac {1}{18} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}-\frac {2 \left (8 e^{6 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}}-\frac {2 e^{6 c_1}}{9 x^6}+\frac {8}{81}}-\frac {1}{9}\right )\right \},\left \{y(x)\to -x^3 \left (\frac {1}{2} \sqrt {\frac {2 \left (8 e^{6 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}}+\frac {1}{18} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}-\frac {e^{6 c_1}}{9 x^6}+\frac {4}{81}}+\frac {1}{2} \sqrt {-\frac {\frac {64}{729}+\frac {64 e^{6 c_1}}{27 x^6}}{4 \sqrt {\frac {2 \left (8 e^{6 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}}+\frac {1}{18} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}-\frac {e^{6 c_1}}{9 x^6}+\frac {4}{81}}}-\frac {1}{18} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}-\frac {2 \left (8 e^{6 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}}-\frac {2 e^{6 c_1}}{9 x^6}+\frac {8}{81}}-\frac {1}{9}\right )\right \},\left \{y(x)\to -x^3 \left (-\frac {1}{2} \sqrt {\frac {2 \left (8 e^{6 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}}+\frac {1}{18} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}-\frac {e^{6 c_1}}{9 x^6}+\frac {4}{81}}-\frac {1}{2} \sqrt {\frac {\frac {64}{729}+\frac {64 e^{6 c_1}}{27 x^6}}{4 \sqrt {\frac {2 \left (8 e^{6 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}}+\frac {1}{18} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}-\frac {e^{6 c_1}}{9 x^6}+\frac {4}{81}}}-\frac {1}{18} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}-\frac {2 \left (8 e^{6 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}}-\frac {2 e^{6 c_1}}{9 x^6}+\frac {8}{81}}-\frac {1}{9}\right )\right \},\left \{y(x)\to -x^3 \left (-\frac {1}{2} \sqrt {\frac {2 \left (8 e^{6 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}}+\frac {1}{18} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}-\frac {e^{6 c_1}}{9 x^6}+\frac {4}{81}}+\frac {1}{2} \sqrt {\frac {\frac {64}{729}+\frac {64 e^{6 c_1}}{27 x^6}}{4 \sqrt {\frac {2 \left (8 e^{6 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}}+\frac {1}{18} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}-\frac {e^{6 c_1}}{9 x^6}+\frac {4}{81}}}-\frac {1}{18} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}-\frac {2 \left (8 e^{6 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {64 \sqrt {e^{12 c_1} x^{60}-3 e^{18 c_1} x^{54}+3 e^{24 c_1} x^{48}-e^{30 c_1} x^{42}}}{x^{36}}+\frac {64 e^{6 c_1}}{x^6}+\frac {160 e^{12 c_1}}{x^{12}}-\frac {8 e^{18 c_1}}{x^{18}}}}-\frac {2 e^{6 c_1}}{9 x^6}+\frac {8}{81}}-\frac {1}{9}\right )\right \},\left \{y(x)\to -x^3 \left (\frac {1}{2} \sqrt {\frac {e^{-24 c_1} \left (8 e^{18 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}}+\frac {1}{9} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}-\frac {e^{-6 c_1}}{9 x^6}+\frac {4}{81}}-\frac {1}{2} \sqrt {-\frac {\frac {64}{729}+\frac {64 e^{-6 c_1}}{27 x^6}}{4 \sqrt {\frac {e^{-24 c_1} \left (8 e^{18 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}}+\frac {1}{9} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}-\frac {e^{-6 c_1}}{9 x^6}+\frac {4}{81}}}-\frac {1}{9} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}-\frac {e^{-24 c_1} \left (8 e^{18 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}}-\frac {2 e^{-6 c_1}}{9 x^6}+\frac {8}{81}}-\frac {1}{9}\right )\right \},\left \{y(x)\to -x^3 \left (\frac {1}{2} \sqrt {\frac {e^{-24 c_1} \left (8 e^{18 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}}+\frac {1}{9} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}-\frac {e^{-6 c_1}}{9 x^6}+\frac {4}{81}}+\frac {1}{2} \sqrt {-\frac {\frac {64}{729}+\frac {64 e^{-6 c_1}}{27 x^6}}{4 \sqrt {\frac {e^{-24 c_1} \left (8 e^{18 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}}+\frac {1}{9} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}-\frac {e^{-6 c_1}}{9 x^6}+\frac {4}{81}}}-\frac {1}{9} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}-\frac {e^{-24 c_1} \left (8 e^{18 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}}-\frac {2 e^{-6 c_1}}{9 x^6}+\frac {8}{81}}-\frac {1}{9}\right )\right \},\left \{y(x)\to -x^3 \left (-\frac {1}{2} \sqrt {\frac {e^{-24 c_1} \left (8 e^{18 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}}+\frac {1}{9} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}-\frac {e^{-6 c_1}}{9 x^6}+\frac {4}{81}}-\frac {1}{2} \sqrt {\frac {\frac {64}{729}+\frac {64 e^{-6 c_1}}{27 x^6}}{4 \sqrt {\frac {e^{-24 c_1} \left (8 e^{18 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}}+\frac {1}{9} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}-\frac {e^{-6 c_1}}{9 x^6}+\frac {4}{81}}}-\frac {1}{9} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}-\frac {e^{-24 c_1} \left (8 e^{18 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}}-\frac {2 e^{-6 c_1}}{9 x^6}+\frac {8}{81}}-\frac {1}{9}\right )\right \},\left \{y(x)\to -x^3 \left (-\frac {1}{2} \sqrt {\frac {e^{-24 c_1} \left (8 e^{18 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}}+\frac {1}{9} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}-\frac {e^{-6 c_1}}{9 x^6}+\frac {4}{81}}+\frac {1}{2} \sqrt {\frac {\frac {64}{729}+\frac {64 e^{-6 c_1}}{27 x^6}}{4 \sqrt {\frac {e^{-24 c_1} \left (8 e^{18 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}}+\frac {1}{9} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}-\frac {e^{-6 c_1}}{9 x^6}+\frac {4}{81}}}-\frac {1}{9} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}-\frac {e^{-24 c_1} \left (8 e^{18 c_1} x^{18}+e^{12 c_1} x^{12}\right )}{9 x^{24} \sqrt [3]{\frac {8 e^{-36 c_1} \sqrt {e^{60 c_1} x^{60}-3 e^{54 c_1} x^{54}+3 e^{48 c_1} x^{48}-e^{42 c_1} x^{42}}}{x^{36}}+\frac {8 e^{-6 c_1}}{x^6}+\frac {20 e^{-12 c_1}}{x^{12}}-\frac {e^{-18 c_1}}{x^{18}}}}-\frac {2 e^{-6 c_1}}{9 x^6}+\frac {8}{81}}-\frac {1}{9}\right )\right \}\right \}$ Maple : cpu = 0.576 (sec), leaf count = 169

$\left \{ y \left ( x \right ) ={\frac {{x}^{4}- \left ( {\it RootOf} \left ( {x}^{16}-12\,{{\it \_Z}}^{2}{x}^{12}-16\,{{\it \_Z}}^{3}{x}^{10}+30\,{{\it \_Z}}^{4}{x}^{8}+96\,{{\it \_Z}}^{5}{x}^{6}+100\,{{\it \_Z}}^{6}{x}^{4}+48\,{{\it \_Z}}^{7}{x}^{2}+9\,{{\it \_Z}}^{8}-16\,{\it \_C1}\,{x}^{4} \right ) \right ) ^{2}}{2\,x}},y \left ( x \right ) ={\frac {{x}^{4}- \left ( {\it RootOf} \left ( {\it \_C1}\,{x}^{16}-12\,{\it \_C1}\,{{\it \_Z}}^{2}{x}^{12}+16\,{\it \_C1}\,{{\it \_Z}}^{3}{x}^{10}+30\,{\it \_C1}\,{{\it \_Z}}^{4}{x}^{8}-96\,{\it \_C1}\,{{\it \_Z}}^{5}{x}^{6}+100\,{\it \_C1}\,{{\it \_Z}}^{6}{x}^{4}-48\,{\it \_C1}\,{{\it \_Z}}^{7}{x}^{2}+9\,{\it \_C1}\,{{\it \_Z}}^{8}-16\,{x}^{4} \right ) \right ) ^{2}}{2\,x}} \right \}$