8.43   ODE No. 1633

\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +ay \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +b \left ( y \left ( x \right ) \right ) ^{3}=0} \]

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

Mathematica: cpu = 35.438000 (sec), leaf count = 25 \[ \text {DSolve}\left [a y(x) y'(x)+b y(x)^3+y''(x)=0,y(x),x\right ] \]

Maple: cpu = 0.188 (sec), leaf count = 97 \[ \left \{ \int ^{y \left ( x \right ) }\! \left ( {\it RootOf} \left ( -2\, a{{\it \_a}}^{2}{\it Artanh} \left ( {\frac {{{\it \_a}}^{2}a+4\,{\it \_Z}}{\sqrt {{{\it \_a}}^{4} \left ( {a}^{2}-8\,b \right ) }}} \right ) - \ln \left ( {{\it \_a}}^{4}b+{\it \_Z}\,{{\it \_a}}^{2}a+2\,{{\it \_Z} }^{2} \right ) \sqrt {{{\it \_a}}^{4} \left ( {a}^{2}-8\,b \right ) }+{ \it \_C1}\,\sqrt {{{\it \_a}}^{4} \left ( {a}^{2}-8\,b \right ) } \right ) \right ) ^{-1}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]