3.563   ODE No. 563

\[ \boxed { \ln \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) +x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +ay \left ( x \right ) +b=0} \]

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

Mathematica: cpu = 0.108514 (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 = 0.125 (sec), leaf count = 66 \[ \left \{ - \left ( {{\rm e}^{-ay \left ( x \right ) -{\it lambertW} \left ( x{{\rm e}^{-ay \left ( x \right ) -b}} \right ) -b}} \right ) ^{- \left ( a+1 \right ) ^{-1}}{\it \_C1}+x-{\frac {{{\rm e}^{ay \left ( x \right ) +{\it lambertW} \left ( x{{\rm e}^{-ay \left ( x \right ) -b}} \right ) +b}}}{a}}=0 \right \} \]