2.1700   ODE No. 1700

\[ y(x) y''(x)-y'(x)^2+1=0 \] Mathematica : cpu = 0.176879 (sec), leaf count = 44


\[\left \{\left \{y(x)\to -e^{-c_1} \sinh \left (e^{c_1} (x+c_2)\right )\right \},\left \{y(x)\to e^{-c_1} \sinh \left (e^{c_1} (x+c_2)\right )\right \}\right \}\] Maple : cpu = 1.13 (sec), leaf count = 86


\[y \relax (x ) = \frac {\left (-c_{1} {\mathrm e}^{\frac {2 x}{c_{1}}} {\mathrm e}^{\frac {2 c_{2}}{c_{1}}}+c_{1}\right ) {\mathrm e}^{-\frac {c_{2}}{c_{1}}} {\mathrm e}^{-\frac {x}{c_{1}}}}{2}\]