8.113   ODE No. 1703

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

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

Mathematica: cpu = 0.094512 (sec), leaf count = 63 \[ \left \{\left \{y(x)\to e^{\frac {1}{2} \left (e^{c_2+x}-c_1 e^{-c_2-x}\right )}\right \},\left \{y(x)\to e^{\frac {1}{2} \left (e^{-c_2-x}-c_1 e^{c_2+x}\right )}\right \}\right \} \]

Maple: cpu = 0.047 (sec), leaf count = 25 \[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {{{\rm e}^{2\,x}}{\it \_C1}}{2\,{{\rm e}^{x}}}}}}{{\rm e}^{{\frac {{\it \_C2}}{2\,{{\rm e}^{ x}}}}}} \right \} \]