3.869   ODE No. 869

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {-x+1-2\,y \left ( x \right ) +3\,{x}^{2}-2\,{x}^{2}y \left ( x \right ) +2\,{x}^{4}+{x}^{3}-2\,{x}^{3}y \left ( x \right ) +2\,{x}^{5}}{{x}^{2}-y \left ( x \right ) }}=0} \]

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

Mathematica: cpu = 0.035005 (sec), leaf count = 42 \[ \left \{\left \{y(x)\to \frac {1}{2} \left (W\left (-e^{c_1+x^4+\frac {4 x^3}{3}-2 x^2+4 x-1}\right )+1\right )+x^2\right \}\right \} \]

Maple: cpu = 0.047 (sec), leaf count = 37 \[ \left \{ y \left ( x \right ) ={x}^{2}+{\frac {1}{2}{\it lambertW} \left ( -2\,{\frac {{{\rm e}^{{x}^{4}}}{{\rm e}^{4/3\,{x}^{3}}}{\it \_C1}\, \left ( {{\rm e}^{x}} \right ) ^{4}{{\rm e}^{-1}}}{ \left ( { {\rm e}^{{x}^{2}}} \right ) ^{2}}} \right ) }+{\frac {1}{2}} \right \} \]