2.565   ODE No. 565

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

\[ y'(x)+y(x) \log \left (y'(x)\right )-x y(x)-y(x) \log (y(x))=0 \] Mathematica : cpu = 0.0170926 (sec), leaf count = 25

\[\left \{\left \{y(x)\to c_1 e^{\frac {1}{2} W\left (e^x\right )^2+W\left (e^x\right )}\right \}\right \}\] Maple : cpu = 0.303 (sec), leaf count = 17

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{{\frac {{\it lambertW} \left ( {{\rm e}^{x}} \right ) \left ( {\it lambertW} \left ( {{\rm e}^{x}} \right ) +2 \right ) }{2}}}} \right \} \]