\[ -f(x) y(x) y'(x)-g(x) y(x)^2-y'(x)^2+y(x) y''(x)=0 \] ✓ Mathematica : cpu = 0.0587175 (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 = 0.399 (sec), leaf count = 61
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C2}}{{{\rm e}^{{\it \_C1}\,\int \!{{\rm e}^{\int \!f \left ( x \right ) \,{\rm d}x}}\,{\rm d}x}}}{{\rm e}^{\int \!{{\rm e}^{\int \!f \left ( x \right ) \,{\rm d}x}}\,{\rm d}x\int \!{\frac {g \left ( x \right ) }{{{\rm e}^{\int \!f \left ( x \right ) \,{\rm d}x}}}}\,{\rm d}x}} \left ( {{\rm e}^{\int \!{\frac {\int \!{{\rm e}^{\int \!f \left ( x \right ) \,{\rm d}x}}\,{\rm d}xg \left ( x \right ) }{{{\rm e}^{\int \!f \left ( x \right ) \,{\rm d}x}}}}\,{\rm d}x}} \right ) ^{-1}} \right \} \]