3.117   ODE No. 117

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

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

Mathematica: cpu = 0.024503 (sec), leaf count = 21 \[ \left \{\left \{y(x)\to -x \log \left (\frac {e^{-c_1}}{x}-1\right )\right \}\right \} \]

Maple: cpu = 0.078 (sec), leaf count = 20 \[ \left \{ y \left ( x \right ) = \left ( \ln \left ( -{\frac {x}{-1+x{ {\rm e}^{{\it \_C1}}}}} \right ) +{\it \_C1} \right ) x \right \} \]