2.1029   ODE No. 1029

\[ y''(x)-y(x) \left (f'(x)+f(x)^2\right )=0 \] Mathematica : cpu = 0.0211334 (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 = 0.115 (sec), leaf count = 22


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