\[ -f(x) y(x) y'(x)-g(x) y(x)^2+y(x) y''(x)-y'(x)^2=0 \] ✓ Mathematica : cpu = 0.101042 (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 = 0.266 (sec), leaf count = 61
\[\{y \left (x \right ) = c_{2} {\mathrm e}^{\left (\int {\mathrm e}^{\int -f \left (x \right )d x} g \left (x \right )d x \right ) \left (\int {\mathrm e}^{\int f \left (x \right )d x}d x \right )} {\mathrm e}^{\int \left (\int -{\mathrm e}^{\int f \left (x \right )d x}d x \right ) {\mathrm e}^{\int -f \left (x \right )d x} g \left (x \right )d x} {\mathrm e}^{\int -c_{1} {\mathrm e}^{\int f \left (x \right )d x}d x}\}\]