\[ y(x) y''(x)-y'(x)^2-1=0 \] ✓ Mathematica : cpu = 0.202521 (sec), leaf count = 80
\[\left \{\left \{y(x)\to -\frac {e^{-c_1} \tanh \left (e^{c_1} (x+c_2)\right )}{\sqrt {-1+\tanh ^2\left (e^{c_1} (x+c_2)\right )}}\right \},\left \{y(x)\to \frac {e^{-c_1} \tanh \left (e^{c_1} (x+c_2)\right )}{\sqrt {-1+\tanh ^2\left (e^{c_1} (x+c_2)\right )}}\right \}\right \}\] ✓ Maple : cpu = 1.08 (sec), leaf count = 42
\[y \relax (x ) = \frac {c_{1} \left ({\mathrm e}^{\frac {2 c_{2}}{c_{1}}} {\mathrm e}^{\frac {2 x}{c_{1}}}+1\right ) {\mathrm e}^{-\frac {c_{2}}{c_{1}}} {\mathrm e}^{-\frac {x}{c_{1}}}}{2}\]