\[ a^2 y(x)^2 \left (\log ^2(y(x))-1\right )+y'(x)^2=0 \] ✓ Mathematica : cpu = 0.295552 (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 = 0.186 (sec), leaf count = 49
\[ \left \{ y \left ( x \right ) = \left ( {{\rm e}^{-\sin \left ( a \left ( x-{\it \_C1} \right ) \right ) }} \right ) ^{-1},y \left ( x \right ) ={{\rm e}^{-\sin \left ( a \left ( x-{\it \_C1} \right ) \right ) }},y \left ( x \right ) ={{\rm e}^{{\it RootOf} \left ( {a}^{2} \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2} \left ( {{\it \_Z}}^{2}-1 \right ) \right ) }} \right \} \]