\[ y'(x)=\frac {y(x) (y(x)+x+1)}{(x+1) \left (y(x)^4+y(x)^3+y(x)^2+x\right )} \] ✓ Mathematica : cpu = 3.6994 (sec), leaf count = 2405
\[\left \{\left \{y(x)\to \frac {1}{8} \left (-4 \sqrt {\frac {-8 x+3 c_1+3 \log (x+1)+2}{\sqrt [3]{36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}}+\frac {1}{2} \sqrt [3]{36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}-\frac {23}{16}}-4 \sqrt {\frac {8 x-3 c_1-3 \log (x+1)-2}{\sqrt [3]{36 c_1^2+72 \log (x+1) c_1+18 c_1+36 \log ^2(x+1)+69 x+18 \log (x+1)+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}}-\frac {1}{2} \sqrt [3]{36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}-\frac {24 \left (c_1+\log (x+1)\right )+\frac {117}{8}}{4 \sqrt {\frac {-8 x+3 c_1+3 \log (x+1)+2}{\sqrt [3]{36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}}+\frac {1}{2} \sqrt [3]{36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}-\frac {23}{16}}}-\frac {23}{8}}-3\right )\right \},\left \{y(x)\to \frac {1}{8} \left (-4 \sqrt {\frac {-8 x+3 c_1+3 \log (x+1)+2}{\sqrt [3]{36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}}+\frac {1}{2} \sqrt [3]{36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}-\frac {23}{16}}+4 \sqrt {\frac {8 x-3 c_1-3 \log (x+1)-2}{\sqrt [3]{36 c_1^2+72 \log (x+1) c_1+18 c_1+36 \log ^2(x+1)+69 x+18 \log (x+1)+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}}-\frac {1}{2} \sqrt [3]{36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}-\frac {24 \left (c_1+\log (x+1)\right )+\frac {117}{8}}{4 \sqrt {\frac {-8 x+3 c_1+3 \log (x+1)+2}{\sqrt [3]{36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}}+\frac {1}{2} \sqrt [3]{36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}-\frac {23}{16}}}-\frac {23}{8}}-3\right )\right \},\left \{y(x)\to \frac {1}{8} \left (4 \sqrt {\frac {-8 x+3 c_1+3 \log (x+1)+2}{\sqrt [3]{36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}}+\frac {1}{2} \sqrt [3]{36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}-\frac {23}{16}}-4 \sqrt {\frac {8 x-3 c_1-3 \log (x+1)-2}{\sqrt [3]{36 c_1^2+72 \log (x+1) c_1+18 c_1+36 \log ^2(x+1)+69 x+18 \log (x+1)+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}}-\frac {1}{2} \sqrt [3]{36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}+\frac {24 \left (c_1+\log (x+1)\right )+\frac {117}{8}}{4 \sqrt {\frac {-8 x+3 c_1+3 \log (x+1)+2}{\sqrt [3]{36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}}+\frac {1}{2} \sqrt [3]{36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}-\frac {23}{16}}}-\frac {23}{8}}-3\right )\right \},\left \{y(x)\to \frac {1}{8} \left (4 \sqrt {\frac {-8 x+3 c_1+3 \log (x+1)+2}{\sqrt [3]{36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}}+\frac {1}{2} \sqrt [3]{36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}-\frac {23}{16}}+4 \sqrt {\frac {8 x-3 c_1-3 \log (x+1)-2}{\sqrt [3]{36 c_1^2+72 \log (x+1) c_1+18 c_1+36 \log ^2(x+1)+69 x+18 \log (x+1)+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}}-\frac {1}{2} \sqrt [3]{36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}+\frac {24 \left (c_1+\log (x+1)\right )+\frac {117}{8}}{4 \sqrt {\frac {-8 x+3 c_1+3 \log (x+1)+2}{\sqrt [3]{36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}}+\frac {1}{2} \sqrt [3]{36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+\sqrt {\left (36 \left (c_1+\log (x+1)\right ){}^2+18 \left (c_1+\log (x+1)\right )+69 x+8\right ){}^2-8 \left (-8 x+3 \left (c_1+\log (x+1)\right )+2\right ){}^3}+8}-\frac {23}{16}}}-\frac {23}{8}}-3\right )\right \}\right \}\]
✓ Maple : cpu = 0.199 (sec), leaf count = 31
\[ \left \{ \ln \left ( 1+x \right ) +{\frac {x}{y \left ( x \right ) }}-{\frac { \left ( y \left ( x \right ) \right ) ^{3}}{3}}-{\frac { \left ( y \left ( x \right ) \right ) ^{2}}{2}}-y \left ( x \right ) +{\it \_C1}=0 \right \} \]