3.771   ODE No. 771

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {-4\,axy \left ( x \right ) -{a}^{2}{x}^{3}-2\,a{x}^{2}b-4\,ax+8}{8\,y \left ( x \right ) +2\,a{x}^{2}+4\,bx+8}}=0} \]

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

Mathematica: cpu = 0.053007 (sec), leaf count = 46 \[ \left \{\left \{y(x)\to \frac {1}{4} \left (-a x^2-2 b x-4\right )-\frac {2 \left (W\left (-e^{-\frac {b^2 x}{4}+c_1-1}\right )+1\right )}{b}\right \}\right \} \]

Maple: cpu = 0.078 (sec), leaf count = 84 \[ \left \{ y \left ( x \right ) ={\frac {1}{4\,b} \left ( -a{x}^{2}b-2\,{b} ^{2}x-4\,b+4\,{{\rm e}^{-1/4\,{\frac {1}{a} \left ( a{b}^{2}x+2\,{\it \_C1}\,{b}^{2}+4\,{\it lambertW} \left ( -1/2\,{{\rm e}^{-1/4\,{b}^{2}x }}{{\rm e}^{-1/2\,{\frac {{\it \_C1}\,{b}^{2}}{a}}}}{{\rm e}^{-b/2}}{ {\rm e}^{-1}} \right ) a+2\,ab+4\,a \right ) }}}-8 \right ) } \right \} \]