\[ \boxed { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+{a}^{2} \left ( y \left ( x \right ) \right ) ^{2} \left ( \left ( \ln \left ( y \left ( x \right ) \right ) \right ) ^{2}-1 \right ) =0} \]
Mathematica: cpu = 0.109014 (sec), leaf count = 71 \[ \left \{\left \{y(x)\to e^{\frac {1}{2} \left (e^{-c_1+i a x}+e^{c_1-i a x}\right )}\right \},\left \{y(x)\to \exp \left (\frac {1}{2} \left (e^{-c_1-i a x}+e^{c_1+i a x}\right )\right )\right \}\right \} \]
Maple: cpu = 0.187 (sec), leaf count = 47 \[ \left \{ y \left ( x \right ) = \left ( {{\rm e}^{\sin \left ( {\it \_C1} \,a-ax \right ) }} \right ) ^{-1},y \left ( x \right ) ={{\rm e}^{{\it RootOf} \left ( {a}^{2} \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2} \left ( {{\it \_Z}}^{2}-1 \right ) \right ) }},y \left ( x \right ) ={ {\rm e}^{\sin \left ( {\it \_C1}\,a-ax \right ) }} \right \} \]