2.341   ODE No. 341

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

\[ \left (\text {Global$\grave { }$x} e^{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})}+e^{\text {Global$\grave { }$x}}\right ) \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})+e^{\text {Global$\grave { }$x}} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})+e^{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})}=0 \] Mathematica : cpu = 0.0504487 (sec), leaf count = 33

\[\left \{\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to c_1 e^{-\text {Global$\grave { }$x}}-W\left (\text {Global$\grave { }$x} e^{c_1 e^{-\text {Global$\grave { }$x}}-\text {Global$\grave { }$x}}\right )\right \}\right \}\]

Maple : cpu = 0.061 (sec), leaf count = 30

\[ \left \{ y \left ( x \right ) =-{\it lambertW} \left ( {\frac {x}{{{\rm e}^{x}}} \left ( {{\rm e}^{{\frac {{\it \_C1}}{{{\rm e}^{x}}}}}} \right ) ^{-1}} \right ) -{\frac {{\it \_C1}}{{{\rm e}^{x}}}} \right \} \]