2.1631   ODE No. 1631

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

\[ -(f(x)+3 y(x)) y'(x)+f(x) y(x)^2+y''(x)+y(x)^3=0 \] Mathematica : cpu = 0.0186553 (sec), leaf count = 0 , could not solve

DSolve[f[x]*y[x]^2 + y[x]^3 - (f[x] + 3*y[x])*Derivative[1][y][x] + Derivative[2][y][x] == 0, y[x], x]

Maple : cpu = 0.303 (sec), leaf count = 38

\[ \left \{ y \left ( x \right ) ={\frac {-\int \!{\it \_C1}\,{{\rm e}^{\int \!f \left ( x \right ) \,{\rm d}x}}\,{\rm d}x-{\it \_C2}}{\int \!\!\!\int \!{\it \_C1}\,{{\rm e}^{\int \!f \left ( x \right ) \,{\rm d}x}}\,{\rm d}x\,{\rm d}x+{\it \_C2}\,x+1}} \right \} \]