\[ x \left (x y'(x)-y(x)\right )^2-y'(x)=0 \] ✓ Mathematica : cpu = 0.264066 (sec), leaf count = 3049
DSolve[-Derivative[1][y][x] + x*(-y[x] + x*Derivative[1][y][x])^2 == 0,y[x],x]
\[\left \{\left \{y(x)\to -\frac {1}{2} \sqrt {\frac {16}{9} e^{-6 c_1} x^2+\frac {2 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}}}{9 x^2}+\frac {16 e^{-24 c_1} \left (8 e^{12 c_1} x^8-e^{18 c_1} x^2\right )}{9 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}} x^2}+\frac {1}{81 x^4}}-\frac {1}{2} \sqrt {\frac {32}{9} e^{-6 c_1} x^2-\frac {\frac {512 e^{-6 c_1}}{27}-\frac {8}{729 x^6}}{4 \sqrt {\frac {16}{9} e^{-6 c_1} x^2+\frac {2 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}}}{9 x^2}+\frac {16 e^{-24 c_1} \left (8 e^{12 c_1} x^8-e^{18 c_1} x^2\right )}{9 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}} x^2}+\frac {1}{81 x^4}}}-\frac {2 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}}}{9 x^2}-\frac {16 e^{-24 c_1} \left (8 e^{12 c_1} x^8-e^{18 c_1} x^2\right )}{9 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}} x^2}+\frac {2}{81 x^4}}-\frac {1}{18 x^2}\right \},\left \{y(x)\to -\frac {1}{2} \sqrt {\frac {16}{9} e^{-6 c_1} x^2+\frac {2 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}}}{9 x^2}+\frac {16 e^{-24 c_1} \left (8 e^{12 c_1} x^8-e^{18 c_1} x^2\right )}{9 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}} x^2}+\frac {1}{81 x^4}}+\frac {1}{2} \sqrt {\frac {32}{9} e^{-6 c_1} x^2-\frac {\frac {512 e^{-6 c_1}}{27}-\frac {8}{729 x^6}}{4 \sqrt {\frac {16}{9} e^{-6 c_1} x^2+\frac {2 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}}}{9 x^2}+\frac {16 e^{-24 c_1} \left (8 e^{12 c_1} x^8-e^{18 c_1} x^2\right )}{9 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}} x^2}+\frac {1}{81 x^4}}}-\frac {2 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}}}{9 x^2}-\frac {16 e^{-24 c_1} \left (8 e^{12 c_1} x^8-e^{18 c_1} x^2\right )}{9 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}} x^2}+\frac {2}{81 x^4}}-\frac {1}{18 x^2}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {\frac {16}{9} e^{-6 c_1} x^2+\frac {2 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}}}{9 x^2}+\frac {16 e^{-24 c_1} \left (8 e^{12 c_1} x^8-e^{18 c_1} x^2\right )}{9 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}} x^2}+\frac {1}{81 x^4}}-\frac {1}{2} \sqrt {\frac {32}{9} e^{-6 c_1} x^2+\frac {\frac {512 e^{-6 c_1}}{27}-\frac {8}{729 x^6}}{4 \sqrt {\frac {16}{9} e^{-6 c_1} x^2+\frac {2 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}}}{9 x^2}+\frac {16 e^{-24 c_1} \left (8 e^{12 c_1} x^8-e^{18 c_1} x^2\right )}{9 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}} x^2}+\frac {1}{81 x^4}}}-\frac {2 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}}}{9 x^2}-\frac {16 e^{-24 c_1} \left (8 e^{12 c_1} x^8-e^{18 c_1} x^2\right )}{9 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}} x^2}+\frac {2}{81 x^4}}-\frac {1}{18 x^2}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {\frac {16}{9} e^{-6 c_1} x^2+\frac {2 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}}}{9 x^2}+\frac {16 e^{-24 c_1} \left (8 e^{12 c_1} x^8-e^{18 c_1} x^2\right )}{9 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}} x^2}+\frac {1}{81 x^4}}+\frac {1}{2} \sqrt {\frac {32}{9} e^{-6 c_1} x^2+\frac {\frac {512 e^{-6 c_1}}{27}-\frac {8}{729 x^6}}{4 \sqrt {\frac {16}{9} e^{-6 c_1} x^2+\frac {2 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}}}{9 x^2}+\frac {16 e^{-24 c_1} \left (8 e^{12 c_1} x^8-e^{18 c_1} x^2\right )}{9 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}} x^2}+\frac {1}{81 x^4}}}-\frac {2 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}}}{9 x^2}-\frac {16 e^{-24 c_1} \left (8 e^{12 c_1} x^8-e^{18 c_1} x^2\right )}{9 \sqrt [3]{512 e^{-18 c_1} x^{12}+160 e^{-12 c_1} x^6-e^{-6 c_1}+e^{-36 c_1} \sqrt {262144 e^{42 c_1} x^{18}+12288 e^{48 c_1} x^{12}+192 e^{54 c_1} x^6+e^{60 c_1}}} x^2}+\frac {2}{81 x^4}}-\frac {1}{18 x^2}\right \}\right \}\] ✓ Maple : cpu = 1.402 (sec), leaf count = 192
dsolve(x*(x*diff(y(x),x)-y(x))^2-diff(y(x),x) = 0,y(x))
\[y \left (x \right ) = \frac {\left (\operatorname {RootOf}\left (-729 x^{12} c_{1}+\textit {\_Z}^{8}-12 \textit {\_Z}^{7}+60 \textit {\_Z}^{6}-160 \textit {\_Z}^{5}+240 \textit {\_Z}^{4}-192 \textit {\_Z}^{3}+64 \textit {\_Z}^{2}\right )-2\right ) \left (\operatorname {RootOf}\left (-729 x^{12} c_{1}+\textit {\_Z}^{8}-12 \textit {\_Z}^{7}+60 \textit {\_Z}^{6}-160 \textit {\_Z}^{5}+240 \textit {\_Z}^{4}-192 \textit {\_Z}^{3}+64 \textit {\_Z}^{2}\right )+1\right )}{9 x^{2}}\]