\[ a^2 y(x)^2 \left (\log ^2(y(x))-1\right )+y'(x)^2=0 \] ✓ Mathematica : cpu = 0.325995 (sec), leaf count = 185
\[\left \{\left \{y(x)\to \exp \left (-\frac {1}{2} \sqrt {-e^{2 i a x-2 c_1}-e^{2 c_1-2 i a x}+2}\right )\right \},\left \{y(x)\to \exp \left (\frac {1}{2} \sqrt {-e^{2 i a x-2 c_1}-e^{2 c_1-2 i a x}+2}\right )\right \},\left \{y(x)\to \exp \left (-\frac {1}{2} \sqrt {-e^{-2 i a x-2 c_1}-e^{2 i a x+2 c_1}+2}\right )\right \},\left \{y(x)\to \exp \left (\frac {1}{2} \sqrt {-e^{-2 i a x-2 c_1}-e^{2 i a x+2 c_1}+2}\right )\right \}\right \}\] ✓ Maple : cpu = 0.238 (sec), leaf count = 49
\[\{y \left (x \right ) = {\mathrm e}^{-\sin \left (\left (-c_{1}+x \right ) a \right )}, y \left (x \right ) = {\mathrm e}^{\RootOf \left (\left (\textit {\_Z}^{2}-1\right ) a^{2} {\mathrm e}^{2 \textit {\_Z}}\right )}, y \left (x \right ) = {\mathrm e}^{\sin \left (a x -c_{1} a \right )}\}\]