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 = 0.041576 (sec), leaf count = 32

\[\left \{\left \{y(x)\to -c_1 \left (W\left (-\frac {e^{-\frac {c_1+c_2+x}{c_1}}}{c_1}\right )+1\right )\right \}\right \}\]

Maple : cpu = 0.096 (sec), leaf count = 33

\[ \left \{ y \left ( x \right ) =-{\it \_C1}\, \left ( {\it lambertW} \left ( -{\frac {{{\rm e}^{-1}}}{{\it \_C1}} \left ( {{\rm e}^{{\frac {{\it \_C2}}{{\it \_C1}}}}} \right ) ^{-1} \left ( {{\rm e}^{{\frac {x}{{\it \_C1}}}}} \right ) ^{-1}} \right ) +1 \right ) \right \} \]