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 = 0.0301469 (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 = 0.257 (sec), leaf count = 17

\[\left \{y \left (x \right ) = c_{1} {\mathrm e}^{\frac {\left (\LambertW \left ({\mathrm e}^{x}\right )+2\right ) \LambertW \left ({\mathrm e}^{x}\right )}{2}}\right \}\]