8.33   ODE No. 1623

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

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

Mathematica: cpu = 0.445557 (sec), leaf count = 50 \[ \text {DSolve}\left [y(x) \left (f'(x)+2 f(x)^2\right )+(3 f(x)+y(x)) y'(x)+f(x) y(x)^2+y''(x)-y(x)^3=0,y(x),x\right ] \]

Maple: cpu = 2.340 (sec), leaf count = 0 \[ \text {could not solve} \]