\[ \boxed { \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) +a \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+b \left ( y \left ( x \right ) \right ) ^{2}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +c \left ( y \left ( x \right ) \right ) ^{4}=0} \]
Mathematica: cpu = 89.226830 (sec), leaf count = 38 \[ \text {DSolve}\left [a y'(x)^2+b y(x)^2 y'(x)+c y(x)^4+y(x) y''(x)=0,y(x),x\right ] \]
Maple: cpu = 1.747 (sec), leaf count = 174 \[ \left \{ \int ^{y \left ( x \right ) }\!{(2\,a+4) \left ( \tan \left ( { \it RootOf} \left ( 2\,{\it \_Z}\,b{{\it \_a}}^{2}-2\,a\ln \left ( { \it \_a} \right ) \sqrt {{{\it \_a}}^{4} \left ( 4\,ac-{b}^{2}+8\,c \right ) }-\ln \left ( {\frac {{{\it \_a}}^{4} \left ( 4\,ac \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}-{b}^{2} \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+8\,c \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+4\,ac-{b}^{2}+8\,c \right ) }{4\,a+8}} \right ) \sqrt {{{\it \_a}}^{4} \left ( 4\,ac-{b}^{2}+8\,c \right ) }+{ \it \_C1}\,\sqrt {{{\it \_a}}^{4} \left ( 4\,ac-{b}^{2}+8\,c \right ) } \right ) \right ) \sqrt {{{\it \_a}}^{4} \left ( 4\,ac-{b}^{2}+8\,c \right ) }-b{{\it \_a}}^{2} \right ) ^{-1}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]