2.1029   ODE No. 1029

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

\[ y''(x)-y(x) \left (f'(x)+f(x)^2\right )=0 \] Mathematica : cpu = 0.0229259 (sec), leaf count = 58

\[\left \{\left \{y(x)\to c_1 \exp \left (\int _1^xf(K[1])dK[1]\right )+c_2 \exp \left (\int _1^xf(K[2])dK[2]\right ) \int _1^x\exp \left (\int _1^{K[4]}-2 f(K[3])dK[3]\right )dK[4]\right \}\right \}\] Maple : cpu = 0.136 (sec), leaf count = 22

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