\[ a y(x) y''(x)+b y'(x)^2+\text {c0}+\text {c1} y(x)+\text {c2} y(x)^2+\text {c3} y(x)^3+\text {c4} y(x)^4=0 \] ✗ Mathematica : cpu = 104.071 (sec), leaf count = 0 , could not solve
DSolve[c0 + c1*y[x] + c2*y[x]^2 + c3*y[x]^3 + c4*y[x]^4 + b*Derivative[1][y][x]^2 + a*y[x]*Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 0.369 (sec), leaf count = 418
\[ \left \{ \int ^{y \left ( x \right ) }\!{ \left ( 2\,a+b \right ) \left ( 3\,a+2\,b \right ) \left ( a+b \right ) \left ( a+2\,b \right ) b{{\it \_a}}^{2\,{\frac {b}{a}}}{\frac {1}{\sqrt {-36\, \left ( a+2\,b \right ) \left ( a+2/3\,b \right ) \left ( a+b \right ) \left ( 2/3\, \left ( a+2\,b \right ) \left ( a+b \right ) b \left ( a+b/2 \right ) {\it c3}\,{{\it \_a}}^{{\frac {3\,a+2\,b}{a}}}+ \left ( \left ( a+2\,b \right ) {\it c2}\,b \left ( a+b/2 \right ) {{\it \_a}}^{{\frac {2\,b+2\,a}{a}}}+ \left ( 1/2\,b{\it c4}\, \left ( a+2\,b \right ) {{\it \_a}}^{{\frac {2\,b+4\,a}{a}}}+ \left ( a+b/2 \right ) \left ( 2\,{{\it \_a}}^{{\frac {a+2\,b}{a}}}b{\it c1}+ \left ( {{\it \_a}}^{2\,{\frac {b}{a}}}{\it c0}-{\it \_C1}\,b \right ) \left ( a+2\,b \right ) \right ) \right ) \left ( a+b \right ) \right ) \left ( a+2/3\,b \right ) \right ) {{\it \_a}}^{2\,{\frac {b}{a}}}b \left ( a+b/2 \right ) }}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-6\,{ \left ( a+2\,b \right ) \left ( a+2/3\,b \right ) \left ( a+b \right ) b \left ( a+b/2 \right ) {{\it \_a}}^{2\,{\frac {b}{a}}}{\frac {1}{\sqrt {-36\, \left ( a+2\,b \right ) \left ( a+2/3\,b \right ) \left ( a+b \right ) \left ( 2/3\, \left ( a+2\,b \right ) \left ( a+b \right ) b \left ( a+b/2 \right ) {\it c3}\,{{\it \_a}}^{{\frac {3\,a+2\,b}{a}}}+ \left ( \left ( a+2\,b \right ) {\it c2}\,b \left ( a+b/2 \right ) {{\it \_a}}^{{\frac {2\,b+2\,a}{a}}}+ \left ( 1/2\,b{\it c4}\, \left ( a+2\,b \right ) {{\it \_a}}^{{\frac {2\,b+4\,a}{a}}}+ \left ( a+b/2 \right ) \left ( 2\,{{\it \_a}}^{{\frac {a+2\,b}{a}}}b{\it c1}+ \left ( {{\it \_a}}^{2\,{\frac {b}{a}}}{\it c0}-{\it \_C1}\,b \right ) \left ( a+2\,b \right ) \right ) \right ) \left ( a+b \right ) \right ) \left ( a+2/3\,b \right ) \right ) {{\it \_a}}^{2\,{\frac {b}{a}}}b \left ( a+b/2 \right ) }}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]