\[ y'(x)=\frac {y(x) (y(x)+x+1)}{(x+1) \left (y(x)^4+y(x)^3+y(x)^2+x\right )} \] ✓ Mathematica : cpu = 3.26419 (sec), leaf count = 2323
\[\left \{\left \{y(x)\to \frac {1}{8} \left (-\sqrt {\frac {16 \left (-8 x+3 c_1+3 \log (x+1)+2\right )}{\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}}+8 \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}-23}-\sqrt {2} \sqrt {\frac {8 \left (8 x-3 c_1-3 \log (x+1)-2\right )}{\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}}-4 \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 {3 \left (64 c_1+64 \log (x+1)+39\right )}{\sqrt {\frac {16 \left (-8 x+3 c_1+3 \log (x+1)+2\right )}{\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}}+8 \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}-23}}-23}-3\right )\right \},\left \{y(x)\to \frac {1}{8} \left (-\sqrt {\frac {16 \left (-8 x+3 c_1+3 \log (x+1)+2\right )}{\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}}+8 \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}-23}+\sqrt {2} \sqrt {\frac {8 \left (8 x-3 c_1-3 \log (x+1)-2\right )}{\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}}-4 \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 {3 \left (64 c_1+64 \log (x+1)+39\right )}{\sqrt {\frac {16 \left (-8 x+3 c_1+3 \log (x+1)+2\right )}{\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}}+8 \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}-23}}-23}-3\right )\right \},\left \{y(x)\to \frac {1}{8} \left (\sqrt {\frac {16 \left (-8 x+3 c_1+3 \log (x+1)+2\right )}{\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}}+8 \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}-23}-\sqrt {2} \sqrt {\frac {8 \left (8 x-3 c_1-3 \log (x+1)-2\right )}{\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}}-4 \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 {3 \left (64 c_1+64 \log (x+1)+39\right )}{\sqrt {\frac {16 \left (-8 x+3 c_1+3 \log (x+1)+2\right )}{\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}}+8 \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}-23}}-23}-3\right )\right \},\left \{y(x)\to \frac {1}{8} \left (\sqrt {\frac {16 \left (-8 x+3 c_1+3 \log (x+1)+2\right )}{\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}}+8 \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}-23}+\sqrt {2} \sqrt {\frac {8 \left (8 x-3 c_1-3 \log (x+1)-2\right )}{\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}}-4 \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 {3 \left (64 c_1+64 \log (x+1)+39\right )}{\sqrt {\frac {16 \left (-8 x+3 c_1+3 \log (x+1)+2\right )}{\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}}+8 \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}-23}}-23}-3\right )\right \}\right \}\]
✓ Maple : cpu = 0.214 (sec), leaf count = 31
\[ \left \{ \ln \left ( 1+x \right ) +{\frac {x}{y \left ( x \right ) }}-{\frac { \left ( y \left ( x \right ) \right ) ^{3}}{3}}-{\frac { \left ( y \left ( x \right ) \right ) ^{2}}{2}}-y \left ( x \right ) +{\it \_C1}=0 \right \} \]