8.222   ODE No. 1812

\[ \boxed { y \left ( x \right ) \left ( 1-\ln \left ( y \left ( x \right ) \right ) \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( 1+\ln \left ( y \left ( x \right ) \right ) \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}=0} \]

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

Mathematica: cpu = 0.027003 (sec), leaf count = 29 \[ \left \{\left \{y(x)\to e^{\frac {c_1 x+c_2 c_1-1}{c_1 \left (c_2+x\right )}}\right \}\right \} \]

Maple: cpu = 0.031 (sec), leaf count = 19 \[ \left \{ y \left ( x \right ) ={{\rm e}^{{\frac {{\it \_C1}\,x+{\it \_C2 }-1}{{\it \_C1}\,x+{\it \_C2}}}}} \right \} \]