\[ a y'(x)^2+b y(x)^2 y'(x)+c y(x)^4+y(x) y''(x)=0 \] ✗ Mathematica : cpu = 195.722 (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 = 2.924 (sec), leaf count = 173
\[ \left \{ \int ^{y \left ( x \right ) }\!{(2\,a+4) \left ( \tan \left ( {\it RootOf} \left ( 2\,{\it \_Z}\,{{\it \_a}}^{2}b-2\,a\ln \left ( {\it \_a} \right ) \sqrt {4\,{{\it \_a}}^{4}ac-{{\it \_a}}^{4}{b}^{2}+8\,c{{\it \_a}}^{4}}-\sqrt {4\,{{\it \_a}}^{4}ac-{{\it \_a}}^{4}{b}^{2}+8\,c{{\it \_a}}^{4}}\ln \left ( {\frac {{{\it \_a}}^{4} \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+1 \right ) \left ( 4\,ac-{b}^{2}+8\,c \right ) }{4\,a+8}} \right ) +{\it \_C1}\,\sqrt {4\,{{\it \_a}}^{4}ac-{{\it \_a}}^{4}{b}^{2}+8\,c{{\it \_a}}^{4}} \right ) \right ) \sqrt {{{\it \_a}}^{4} \left ( 4\,a+8 \right ) c-{{\it \_a}}^{4}{b}^{2}}-b{{\it \_a}}^{2} \right ) ^{-1}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]