\[ a y(x) y''(x)+b y'(x)^2+\text {c0}+\text {c1} y(x)+\text {c2} y(x)^2+\text {c3} y(x)^3+\text {c4} y(x)^4=0 \] ✓ Mathematica : cpu = 5.13686 (sec), leaf count = 716
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}-\frac {\sqrt {4 b^5+20 a b^4+35 a^2 b^3+25 a^3 b^2+6 a^4 b}}{\sqrt {4 b^5 c_1 K[1]^{-\frac {2 b}{a}}+20 a b^4 c_1 K[1]^{-\frac {2 b}{a}}+35 a^2 b^3 c_1 K[1]^{-\frac {2 b}{a}}+25 a^3 b^2 c_1 K[1]^{-\frac {2 b}{a}}+6 a^4 b c_1 K[1]^{-\frac {2 b}{a}}-4 b^4 \text {c4} K[1]^4-12 a b^3 \text {c4} K[1]^4-11 a^2 b^2 \text {c4} K[1]^4-3 a^3 b \text {c4} K[1]^4-4 b^4 \text {c3} K[1]^3-14 a b^3 \text {c3} K[1]^3-14 a^2 b^2 \text {c3} K[1]^3-4 a^3 b \text {c3} K[1]^3-4 b^4 \text {c2} K[1]^2-16 a b^3 \text {c2} K[1]^2-19 a^2 b^2 \text {c2} K[1]^2-6 a^3 b \text {c2} K[1]^2-4 b^4 \text {c1} K[1]-18 a b^3 \text {c1} K[1]-26 a^2 b^2 \text {c1} K[1]-12 a^3 b \text {c1} K[1]-6 a^4 \text {c0}-4 b^4 \text {c0}-20 a b^3 \text {c0}-35 a^2 b^2 \text {c0}-25 a^3 b \text {c0}}}dK[1]\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\sqrt {4 b^5+20 a b^4+35 a^2 b^3+25 a^3 b^2+6 a^4 b}}{\sqrt {4 b^5 c_1 K[2]^{-\frac {2 b}{a}}+20 a b^4 c_1 K[2]^{-\frac {2 b}{a}}+35 a^2 b^3 c_1 K[2]^{-\frac {2 b}{a}}+25 a^3 b^2 c_1 K[2]^{-\frac {2 b}{a}}+6 a^4 b c_1 K[2]^{-\frac {2 b}{a}}-4 b^4 \text {c4} K[2]^4-12 a b^3 \text {c4} K[2]^4-11 a^2 b^2 \text {c4} K[2]^4-3 a^3 b \text {c4} K[2]^4-4 b^4 \text {c3} K[2]^3-14 a b^3 \text {c3} K[2]^3-14 a^2 b^2 \text {c3} K[2]^3-4 a^3 b \text {c3} K[2]^3-4 b^4 \text {c2} K[2]^2-16 a b^3 \text {c2} K[2]^2-19 a^2 b^2 \text {c2} K[2]^2-6 a^3 b \text {c2} K[2]^2-4 b^4 \text {c1} K[2]-18 a b^3 \text {c1} K[2]-26 a^2 b^2 \text {c1} K[2]-12 a^3 b \text {c1} K[2]-6 a^4 \text {c0}-4 b^4 \text {c0}-20 a b^3 \text {c0}-35 a^2 b^2 \text {c0}-25 a^3 b \text {c0}}}dK[2]\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 1.138 (sec), leaf count = 418
\[\int _{}^{y \relax (x )}\frac {\textit {\_a}^{\frac {2 b}{a}} b \left (3 a +2 b \right ) \left (2 a +b \right ) \left (a +2 b \right ) \left (a +b \right )}{\sqrt {-36 \left (a +\frac {2 b}{3}\right ) b \left (\frac {2 b \left (a +2 b \right ) \left (a +b \right ) \left (a +\frac {b}{2}\right ) \mathit {c3} \,\textit {\_a}^{\frac {3 a +2 b}{a}}}{3}+\left (b \left (a +2 b \right ) \mathit {c2} \left (a +\frac {b}{2}\right ) \textit {\_a}^{\frac {2 b +2 a}{a}}+\left (\frac {b \mathit {c4} \left (a +2 b \right ) \textit {\_a}^{\frac {2 b +4 a}{a}}}{2}+\left (2 \textit {\_a}^{\frac {a +2 b}{a}} b \mathit {c1} +\left (\textit {\_a}^{\frac {2 b}{a}} \mathit {c0} -c_{1} b \right ) \left (a +2 b \right )\right ) \left (a +\frac {b}{2}\right )\right ) \left (a +b \right )\right ) \left (a +\frac {2 b}{3}\right )\right ) \left (a +2 b \right ) \textit {\_a}^{\frac {2 b}{a}} \left (a +b \right ) \left (a +\frac {b}{2}\right )}}d \textit {\_a} -x -c_{2} = 0\]