\[ y(x) y'(x)^2-2 x y'(x)+y(x)=0 \] ✓ Mathematica : cpu = 2.95138 (sec), leaf count = 433
DSolve[y[x] - 2*x*Derivative[1][y][x] + y[x]*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\text {Solve}\left [-\frac {i \sqrt {\frac {y(x)^2}{x^2}-1} \tan ^{-1}\left (\sqrt {\frac {y(x)^2}{x^2}-1}\right )}{\sqrt {\frac {y(x)}{x}-1} \sqrt {\frac {y(x)}{x}+1}}-i \sqrt {\frac {\frac {y(x)}{x}-1}{\frac {y(x)}{x}+1}} \left (\frac {y(x)}{x}+1\right )+i \sqrt {\frac {y(x)}{x}-1} \sqrt {\frac {y(x)}{x}+1}+\log \left (\frac {y(x)}{x}\right )+\frac {2 i \sqrt {\frac {y(x)}{x}-1} \sin ^{-1}\left (\frac {\sqrt {1-\frac {y(x)}{x}}}{\sqrt {2}}\right )}{\sqrt {1-\frac {y(x)}{x}}}-2 i \tanh ^{-1}\left (\sqrt {\frac {\frac {y(x)}{x}-1}{\frac {y(x)}{x}+1}}\right )=-\log (x)+c_1,y(x)\right ],\text {Solve}\left [\frac {i \sqrt {\frac {y(x)^2}{x^2}-1} \tan ^{-1}\left (\sqrt {\frac {y(x)^2}{x^2}-1}\right )}{\sqrt {\frac {y(x)}{x}-1} \sqrt {\frac {y(x)}{x}+1}}+i \sqrt {\frac {\frac {y(x)}{x}-1}{\frac {y(x)}{x}+1}} \left (\frac {y(x)}{x}+1\right )-i \sqrt {\frac {y(x)}{x}-1} \sqrt {\frac {y(x)}{x}+1}+\log \left (\frac {y(x)}{x}\right )-\frac {2 i \sqrt {\frac {y(x)}{x}-1} \sin ^{-1}\left (\frac {\sqrt {1-\frac {y(x)}{x}}}{\sqrt {2}}\right )}{\sqrt {1-\frac {y(x)}{x}}}+2 i \tanh ^{-1}\left (\sqrt {\frac {\frac {y(x)}{x}-1}{\frac {y(x)}{x}+1}}\right )=-\log (x)+c_1,y(x)\right ]\right \}\] ✓ Maple : cpu = 0.821 (sec), leaf count = 71
dsolve(y(x)*diff(y(x),x)^2-2*x*diff(y(x),x)+y(x) = 0,y(x))
\[y \left (x \right ) = x\]