\[ a y(x)+x y'(x)^2-y(x) y'(x)=0 \] ✓ Mathematica : cpu = 0.843289 (sec), leaf count = 220
DSolve[a*y[x] - y[x]*Derivative[1][y][x] + x*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\text {Solve}\left [-\frac {-\frac {4 a^{3/2} \sqrt {4-\frac {y(x)}{a x}} \sin ^{-1}\left (\frac {\sqrt {\frac {y(x)}{x}}}{2 \sqrt {a}}\right )}{\sqrt {\frac {y(x)}{x}-4 a}}+\sqrt {\frac {y(x)}{x}} \sqrt {\frac {y(x)}{x}-4 a}+\frac {y(x)}{x}}{4 a}=\frac {\log (x)}{2}+c_1,y(x)\right ],\text {Solve}\left [\frac {\frac {4 a^{3/2} \sqrt {4-\frac {y(x)}{a x}} \sin ^{-1}\left (\frac {\sqrt {\frac {y(x)}{x}}}{2 \sqrt {a}}\right )}{\sqrt {\frac {y(x)}{x}-4 a}}-\sqrt {\frac {y(x)}{x}} \sqrt {\frac {y(x)}{x}-4 a}+\frac {y(x)}{x}}{4 a}=-\frac {\log (x)}{2}+c_1,y(x)\right ]\right \}\] ✓ Maple : cpu = 0.057 (sec), leaf count = 42
dsolve(x*diff(y(x),x)^2-y(x)*diff(y(x),x)+a*y(x) = 0,y(x))
\[y \left (x \right ) = 0\]