2.1699   ODE No. 1699

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ y(x) y''(x)+y'(x)^2-y'(x)=0 \] Mathematica : cpu = 0.146007 (sec), leaf count = 40

\[\left \{\left \{y(x)\to c_1 \left (-W\left (-\frac {e^{-\frac {x}{c_1}-1-\frac {c_2}{c_1}}}{c_1}\right )\right )-c_1\right \}\right \}\] Maple : cpu = 1.378 (sec), leaf count = 33

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