3.870   ODE No. 870

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {1}{x} \left ( {{\rm e}^{-{\frac {y \left ( x \right ) }{x}}}}y \left ( x \right ) +{{\rm e}^{-{\frac {y \left ( x \right ) }{x}}}}x+x+{x}^{3}+{x}^{4} \right ) {{\rm e}^{{\frac {y \left ( x \right ) }{x}}}}}=0} \]

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

Mathematica: cpu = 1.681213 (sec), leaf count = 35 \[ \left \{\left \{y(x)\to -x \log \left (\frac {-c_1-\frac {x^4}{4}-\frac {x^3}{3}-x}{x}\right )\right \}\right \} \]

Maple: cpu = 0.702 (sec), leaf count = 30 \[ \left \{ y \left ( x \right ) =-\ln \left ( -{\frac {3\,{x}^{4}+4\,{x}^{ 3}+12\,{\it \_C1}+12\,x}{12\,x}} \right ) x \right \} \]