\[ a y(x) y''(x)+b y'(x)^2+\text {c0}+\text {c1} y(x)+\text {c2} y(x)^2+\text {c3} y(x)^3+\text {c4} y(x)^4=0 \] ✓ Mathematica : cpu = 5.28716 (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 = 1.007 (sec), leaf count = 418
\[ \left \{ \int ^{y \left ( x \right ) }\!{ \left ( 2\,a+b \right ) \left ( 3\,a+2\,b \right ) \left ( a+b \right ) \left ( a+2\,b \right ) b{{\it \_a}}^{2\,{\frac {b}{a}}}{\frac {1}{\sqrt {-36\, \left ( a+2\,b \right ) {{\it \_a}}^{2\,{\frac {b}{a}}} \left ( a+2/3\,b \right ) \left ( 2/3\, \left ( a+2\,b \right ) {\it c3}\, \left ( a+b \right ) b \left ( a+b/2 \right ) {{\it \_a}}^{{\frac {3\,a+2\,b}{a}}}+ \left ( \left ( a+2\,b \right ) b{\it c2}\, \left ( a+b/2 \right ) {{\it \_a}}^{{\frac {2\,b+2\,a}{a}}}+ \left ( 1/2\,b{\it c4}\, \left ( a+2\,b \right ) {{\it \_a}}^{{\frac {2\,b+4\,a}{a}}}+ \left ( 2\,{{\it \_a}}^{{\frac {a+2\,b}{a}}}b{\it c1}+ \left ( {{\it \_a}}^{2\,{\frac {b}{a}}}{\it c0}-{\it \_C1}\,b \right ) \left ( a+2\,b \right ) \right ) \left ( a+b/2 \right ) \right ) \left ( a+b \right ) \right ) \left ( a+2/3\,b \right ) \right ) \left ( a+b \right ) b \left ( a+b/2 \right ) }}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-6\,{ \left ( a+2\,b \right ) \left ( a+2/3\,b \right ) \left ( a+b \right ) b \left ( a+b/2 \right ) {{\it \_a}}^{2\,{\frac {b}{a}}}{\frac {1}{\sqrt {-36\, \left ( a+2\,b \right ) {{\it \_a}}^{2\,{\frac {b}{a}}} \left ( a+2/3\,b \right ) \left ( 2/3\, \left ( a+2\,b \right ) {\it c3}\, \left ( a+b \right ) b \left ( a+b/2 \right ) {{\it \_a}}^{{\frac {3\,a+2\,b}{a}}}+ \left ( \left ( a+2\,b \right ) b{\it c2}\, \left ( a+b/2 \right ) {{\it \_a}}^{{\frac {2\,b+2\,a}{a}}}+ \left ( 1/2\,b{\it c4}\, \left ( a+2\,b \right ) {{\it \_a}}^{{\frac {2\,b+4\,a}{a}}}+ \left ( 2\,{{\it \_a}}^{{\frac {a+2\,b}{a}}}b{\it c1}+ \left ( {{\it \_a}}^{2\,{\frac {b}{a}}}{\it c0}-{\it \_C1}\,b \right ) \left ( a+2\,b \right ) \right ) \left ( a+b/2 \right ) \right ) \left ( a+b \right ) \right ) \left ( a+2/3\,b \right ) \right ) \left ( a+b \right ) b \left ( a+b/2 \right ) }}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]