\[ -2 x^2 y'(x)+y'(x)^2+2 x y(x)=0 \] ✓ Mathematica : cpu = 0.627675 (sec), leaf count = 6217
DSolve[2*x*y[x] - 2*x^2*Derivative[1][y][x] + Derivative[1][y][x]^2 == 0,y[x],x]
\[\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 = 0.293 (sec), leaf count = 169
dsolve(diff(y(x),x)^2-2*x^2*diff(y(x),x)+2*x*y(x) = 0,y(x))
\[y \left (x \right ) = \frac {x^{4}-\RootOf \left (x^{16}-12 \textit {\_Z}^{2} x^{12}+16 \textit {\_Z}^{3} x^{10}+30 \textit {\_Z}^{4} x^{8}-96 \textit {\_Z}^{5} x^{6}+100 \textit {\_Z}^{6} x^{4}-48 \textit {\_Z}^{7} x^{2}+9 \textit {\_Z}^{8}-16 c_{1} x^{4}\right )^{2}}{2 x}\]