\[ x y'(x)^2+x y'(x)-y(x)=0 \] ✓ Mathematica : cpu = 0.242675 (sec), leaf count = 99
DSolve[-y[x] + x*Derivative[1][y][x] + x*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\text {Solve}\left [\frac {1}{\sqrt {\frac {4 y(x)}{x}+1}-1}-\log \left (1-\sqrt {\frac {4 y(x)}{x}+1}\right )=\frac {\log (x)}{2}+c_1,y(x)\right ],\text {Solve}\left [\frac {1}{\sqrt {\frac {4 y(x)}{x}+1}+1}+\log \left (\sqrt {\frac {4 y(x)}{x}+1}+1\right )=-\frac {\log (x)}{2}+c_1,y(x)\right ]\right \}\] ✓ Maple : cpu = 0.058 (sec), leaf count = 65
dsolve(x*diff(y(x),x)^2+x*diff(y(x),x)-y(x) = 0,y(x))
\[y \left (x \right ) = \frac {\left (1+2 \LambertW \left (-\frac {1}{2 \sqrt {\frac {c_{1}}{x}}}\right )\right ) x}{4 \LambertW \left (-\frac {1}{2 \sqrt {\frac {c_{1}}{x}}}\right )^{2}}\]