2.563   ODE No. 563

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

\[ a y(x)+b+x y'(x)+\log \left (y'(x)\right )=0 \] Mathematica : cpu = 0.231577 (sec), leaf count = 59

\[\text {Solve}\left [a \left (\frac {(a+1) \log \left (1-a W\left (x e^{-a y(x)-b}\right )\right )}{a^2}+\frac {W\left (x e^{-a y(x)-b}\right )}{a}\right )+a y(x)=c_1,y(x)\right ]\] Maple : cpu = 0.225 (sec), leaf count = 66

\[\left \{-c_{1} \left ({\mathrm e}^{-a y \left (x \right )-b -\LambertW \left (x \,{\mathrm e}^{-a y \left (x \right )-b}\right )}\right )^{-\frac {1}{a +1}}+x -\frac {{\mathrm e}^{a y \left (x \right )+b +\LambertW \left (x \,{\mathrm e}^{-a y \left (x \right )-b}\right )}}{a} = 0\right \}\]