ODE No. 757

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

\[ y'(x)=\frac {x^3+2 x^2-4 x y(x)-4 x-8}{2 x^2-8 y(x)+4 x-8} \] Mathematica : cpu = 0.0273327 (sec), leaf count = 36

\[\left \{\left \{y(x)\to 2 \left (W\left (-e^{c_1-\frac {x}{4}-1}\right )+1\right )+\frac {1}{4} \left (x^2+2 x-4\right )\right \}\right \}\] Maple : cpu = 0.072 (sec), leaf count = 26

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