\[ y(x)^2 \log (a y(x))-x y(x) y'(x)+y'(x)^2=0 \] ✓ Mathematica : cpu = 0.197263 (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 = 1.759 (sec), leaf count = 50
\[ \left \{ y \left ( x \right ) ={\frac {1}{a}{{\rm e}^{{\frac {{x}^{2}}{4}}}}},y \left ( x \right ) ={\frac {1}{{{\rm e}^{{{\it \_C1}}^{2}}}{{\rm e}^{{\it \_C1}\,x}}a}},y \left ( x \right ) ={\frac {{{\rm e}^{{\it \_C1}\,x}}}{{{\rm e}^{{{\it \_C1}}^{2}}}a}} \right \} \]