2.1699   ODE No. 1699

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

\[ y'(x)^2-y'(x)+y(x) y''(x)=0 \] Mathematica : cpu = 0.109502 (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 = 0.405 (sec), leaf count = 33

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