\[ a y'(x)^2+b y(x)^2 y'(x)+c y(x)^4+y(x) y''(x)=0 \] ✗ Mathematica : cpu = 93.1708 (sec), leaf count = 0 , could not solve
DSolve[c*y[x]^4 + b*y[x]^2*Derivative[1][y][x] + a*Derivative[1][y][x]^2 + y[x]*Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 0.514 (sec), leaf count = 174
\[ \left \{ \int ^{y \left ( x \right ) }\!{(2\,a+4) \left ( \tan \left ( {\it RootOf} \left ( 2\,{\it \_Z}\,b{{\it \_a}}^{2}-2\,a\ln \left ( {\it \_a} \right ) \sqrt {{{\it \_a}}^{4} \left ( 4\,ac-{b}^{2}+8\,c \right ) }-\ln \left ( {\frac {{{\it \_a}}^{4} \left ( 4\,ac \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}-{b}^{2} \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+8\,c \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+4\,ac-{b}^{2}+8\,c \right ) }{4\,a+8}} \right ) \sqrt {{{\it \_a}}^{4} \left ( 4\,ac-{b}^{2}+8\,c \right ) }+{\it \_C1}\,\sqrt {{{\it \_a}}^{4} \left ( 4\,ac-{b}^{2}+8\,c \right ) } \right ) \right ) \sqrt {{{\it \_a}}^{4} \left ( 4\,ac-{b}^{2}+8\,c \right ) }-b{{\it \_a}}^{2} \right ) ^{-1}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]