\[ -f(x) y(x) y'(x)-g(x) y(x)^2+y(x) y''(x)-y'(x)^2=0 \] ✓ Mathematica : cpu = 0.0668785 (sec), leaf count = 75
DSolve[-(g[x]*y[x]^2) - f[x]*y[x]*Derivative[1][y][x] - Derivative[1][y][x]^2 + y[x]*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_2 \exp \left (\int _1^x\left (\exp \left (\int _1^{K[3]}f(K[1])dK[1]\right ) c_1+\exp \left (\int _1^{K[3]}f(K[1])dK[1]\right ) \int _1^{K[3]}\exp \left (-\int _1^{K[2]}f(K[1])dK[1]\right ) g(K[2])dK[2]\right )dK[3]\right )\right \}\right \}\] ✓ Maple : cpu = 0.189 (sec), leaf count = 61
dsolve(diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2-f(x)*y(x)*diff(y(x),x)-g(x)*y(x)^2=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{\left (\int {\mathrm e}^{\int f \left (x \right )d x}d x \right ) \left (\int {\mathrm e}^{\int -f \left (x \right )d x} g \left (x \right )d x \right )} {\mathrm e}^{\int -c_{1} {\mathrm e}^{\int f \left (x \right )d x}d x} {\mathrm e}^{\int \left (\int -{\mathrm e}^{\int f \left (x \right )d x}d x \right ) {\mathrm e}^{\int -f \left (x \right )d x} g \left (x \right )d x} c_{2}\]