\[ -f(x) y(x) y'(x)-g(x) y(x)^2+y(x) y''(x)-y'(x)^2=0 \] ✓ Mathematica : cpu = 11.0708 (sec), leaf count = 57
\[\left \{\left \{y(x)\to c_2 \exp \left (\int _1^x e^{\int _1^{K[3]} f(K[1]) \, dK[1]} \left (\int _1^{K[3]} g(K[2]) e^{-\int _1^{K[2]} f(K[1]) \, dK[1]} \, dK[2]+c_1\right ) \, dK[3]\right )\right \}\right \}\]
✓ Maple : cpu = 0.092 (sec), leaf count = 61
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C2}}{{{\rm e}^{{\it \_C1}\,\int \!{{\rm e}^{\int \!f \left ( x \right ) \,{\rm d}x}}\,{\rm d}x}}}{{\rm e}^{\int \!{{\rm e}^{\int \!f \left ( x \right ) \,{\rm d}x}}\,{\rm d}x\int \!{\frac {g \left ( x \right ) }{{{\rm e}^{\int \!f \left ( x \right ) \,{\rm d}x}}}}\,{\rm d}x}} \left ( {{\rm e}^{\int \!{\frac {\int \!{{\rm e}^{\int \!f \left ( x \right ) \,{\rm d}x}}\,{\rm d}xg \left ( x \right ) }{{{\rm e}^{\int \!f \left ( x \right ) \,{\rm d}x}}}}\,{\rm d}x}} \right ) ^{-1}} \right \} \]