2.1629   ODE No. 1629

  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 = 0.0685738 (sec), leaf count = 75

\[\left \{\left \{y(x)\to \frac {\int _1^x\exp \left (-\int _1^{K[2]}f(K[1])dK[1]\right ) c_1dK[2]+c_2}{\int _1^x\int _1^{K[5]}\exp \left (-\int _1^{K[4]}f(K[3])dK[3]\right ) c_1dK[4]dK[5]+c_2 x+1}\right \}\right \}\] Maple : cpu = 0.054 (sec), leaf count = 38

\[\left \{y \left (x \right ) = \frac {c_{2}+\int c_{1} {\mathrm e}^{-\left (\int f \left (x \right )d x \right )}d x}{c_{2} x +\int \int c_{1} {\mathrm e}^{-\left (\int f \left (x \right )d x \right )}d x d x +1}\right \}\]