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