3.839   ODE No. 839

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

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

Mathematica: cpu = 0.068009 (sec), leaf count = 28 \[ \left \{\left \{y(x)\to -x \log \left (\frac {e^{2 c_1}}{2 x}-\frac {x}{2}\right )\right \}\right \} \]

Maple: cpu = 0.062 (sec), leaf count = 19 \[ \left \{ y \left ( x \right ) =\ln \left ( 2\,{\frac {x}{-{x}^{2}+{\it \_C1}}} \right ) x \right \} \]