2.1712   ODE No. 1712

\[ -f(x) y(x) y'(x)-g(x) y(x)^2+y(x) y''(x)-y'(x)^2=0 \] Mathematica : cpu = 0.0668785 (sec), leaf count = 75


\[\left \{\left \{y(x)\to c_2 \exp \left (\int _1^x\left (\exp \left (\int _1^{K[3]}f(K[1])dK[1]\right ) c_1+\exp \left (\int _1^{K[3]}f(K[1])dK[1]\right ) \int _1^{K[3]}\exp \left (-\int _1^{K[2]}f(K[1])dK[1]\right ) g(K[2])dK[2]\right )dK[3]\right )\right \}\right \}\] Maple : cpu = 0.189 (sec), leaf count = 61


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