\[ \boxed { \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) - \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-1=0} \]
Mathematica: cpu = 0.180523 (sec), leaf count = 97 \[ \left \{\left \{y(x)\to \frac {1}{2} e^{-e^{c_1} x-2 c_1-e^{c_1} c_2} \left (e^{2 e^{c_1} \left (c_2+x\right )}+e^{2 c_1}\right )\right \},\left \{y(x)\to \frac {1}{2} \left (e^{-e^{c_1} x-2 c_1-e^{c_1} c_2}+e^{e^{c_1} x+e^{c_1} c_2}\right )\right \}\right \} \]
Maple: cpu = 1.654 (sec), leaf count = 79 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{2} \left ( {1 \left ( { {\rm e}^{{\frac {{\it \_C2}}{{\it \_C1}}}}} \right ) ^{-2} \left ( { {\rm e}^{{\frac {x}{{\it \_C1}}}}} \right ) ^{-2}}+1 \right ) {{\rm e}^{ {\frac {{\it \_C2}}{{\it \_C1}}}}}{{\rm e}^{{\frac {x}{{\it \_C1}}}}}} ,y \left ( x \right ) ={\frac {{\it \_C1}}{2} \left ( \left ( {{\rm e}^{{ \frac {{\it \_C2}}{{\it \_C1}}}}} \right ) ^{2} \left ( {{\rm e}^{{ \frac {x}{{\it \_C1}}}}} \right ) ^{2}+1 \right ) \left ( {{\rm e}^{{ \frac {{\it \_C2}}{{\it \_C1}}}}} \right ) ^{-1} \left ( {{\rm e}^{{ \frac {x}{{\it \_C1}}}}} \right ) ^{-1}} \right \} \]