\[ x y'(x)^2-2 y(x)+x=0 \] ✓ Mathematica : cpu = 0.203934 (sec), leaf count = 97
DSolve[x - 2*y[x] + x*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\text {Solve}\left [\frac {2}{\sqrt {\frac {2 y(x)}{x}-1}-1}-2 \log \left (\sqrt {\frac {2 y(x)}{x}-1}-1\right )=\log (x)+c_1,y(x)\right ],\text {Solve}\left [\frac {2}{\sqrt {\frac {2 y(x)}{x}-1}+1}+2 \log \left (\sqrt {\frac {2 y(x)}{x}-1}+1\right )=-\log (x)+c_1,y(x)\right ]\right \}\] ✓ Maple : cpu = 0.523 (sec), leaf count = 73
dsolve(x*diff(y(x),x)^2-2*y(x)+x = 0,y(x))
\[y \left (x \right ) = \left (\frac {\left (\operatorname {LambertW}\left (\frac {\sqrt {x c_{1}}}{c_{1}}\right )+1\right )^{2}}{2 \operatorname {LambertW}\left (\frac {\sqrt {x c_{1}}}{c_{1}}\right )^{2}}+\frac {1}{2}\right ) x\]