2.1633   ODE No. 1633

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

\[ a y(x) y'(x)+b y(x)^3+y''(x)=0 \] Mathematica : cpu = 33.0167 (sec), leaf count = 0 , could not solve

DSolve[b*y[x]^3 + a*y[x]*Derivative[1][y][x] + Derivative[2][y][x] == 0, y[x], x]

Maple : cpu = 1.227 (sec), leaf count = 97

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