\[ y(x)^2 \log (a y(x))-x y(x) y'(x)+y'(x)^2=0 \] ✓ Mathematica : cpu = 0.223711 (sec), leaf count = 27
\[\left \{\left \{y(x)\to \frac {e^{\frac {c_1 x}{2}-\frac {c_1{}^2}{4}}}{a}\right \}\right \}\] ✓ Maple : cpu = 0.502 (sec), leaf count = 50
\[\left \{y \left (x \right ) = \frac {{\mathrm e}^{\frac {x^{2}}{4}}}{a}, y \left (x \right ) = \frac {{\mathrm e}^{c_{1} x} {\mathrm e}^{-c_{1}^{2}}}{a}, y \left (x \right ) = \frac {{\mathrm e}^{-c_{1}^{2}} {\mathrm e}^{-c_{1} x}}{a}\right \}\]