8.124   ODE No. 1714

\[ \boxed { \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) -3\, \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+3\,y \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{2}=0} \]

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

Mathematica: cpu = 0.060508 (sec), leaf count = 25 \[ \left \{\left \{y(x)\to \frac {c_2 e^x}{\sqrt {1-2 e^{c_1+x}}}\right \}\right \} \]

Maple: cpu = 1.513 (sec), leaf count = 67 \[ \left \{ y \left ( x \right ) =-{\frac {\sqrt {2}}{2\,{\it \_C1}\,{ {\rm e}^{x}}-2\,{\it \_C2}}\sqrt { \left ( {\it \_C1}\,{{\rm e}^{x}}-{ \it \_C2} \right ) {{\rm e}^{2\,x}}}},y \left ( x \right ) ={\frac { \sqrt {2}}{2\,{\it \_C1}\,{{\rm e}^{x}}-2\,{\it \_C2}}\sqrt { \left ( { \it \_C1}\,{{\rm e}^{x}}-{\it \_C2} \right ) {{\rm e}^{2\,x}}}} \right \} \]