\[ y(x)^2 \log (a y(x))-x y(x) y'(x)+y'(x)^2=0 \] ✓ Mathematica : cpu = 0.254525 (sec), leaf count = 25
\[\left \{\left \{y(x)\to \frac {e^{\frac {1}{4} c_1 \left (2 x-c_1\right )}}{a}\right \}\right \}\]
✓ Maple : cpu = 1.853 (sec), leaf count = 50
\[ \left \{ y \left ( x \right ) ={\frac {1}{a}{{\rm e}^{{\frac {{x}^{2}}{4}}}}},y \left ( x \right ) ={\frac {1}{{{\rm e}^{{{\it \_C1}}^{2}}}{{\rm e}^{{\it \_C1}\,x}}a}},y \left ( x \right ) ={\frac {{{\rm e}^{{\it \_C1}\,x}}}{{{\rm e}^{{{\it \_C1}}^{2}}}a}} \right \} \]