2.771   ODE No. 771

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

\[ y'(x)=\frac {-a^2 x^3-2 a b x^2-4 a x y(x)-4 a x+8}{2 a x^2+4 b x+8 y(x)+8} \] Mathematica : cpu = 0.0307011 (sec), leaf count = 46

\[\left \{\left \{y(x)\to \frac {1}{4} \left (-a x^2-2 b x-4\right )-\frac {2 \left (1+W\left (-e^{-\frac {b^2 x}{4}-1+c_1}\right )\right )}{b}\right \}\right \}\] Maple : cpu = 0.472 (sec), leaf count = 84

\[ \left \{ y \left ( x \right ) ={\frac {1}{4\,b} \left ( -a{x}^{2}b-2\,{b}^{2}x-4\,b+4\,{{\rm e}^{1/4\,{\frac {1}{a} \left ( -4\,{\it lambertW} \left ( -1/2\,{{\rm e}^{-1/4\,{b}^{2}x}}{{\rm e}^{-1/2\,{\frac {{\it \_C1}\,{b}^{2}}{a}}}}{{\rm e}^{-b/2}}{{\rm e}^{-1}} \right ) a+ \left ( -{b}^{2}x-2\,b-4 \right ) a-2\,{\it \_C1}\,{b}^{2} \right ) }}}-8 \right ) } \right \} \]