\[ y'(x)=-\frac {x \left (64 x^9-288 x^8 y(x)-96 x^8+432 x^7 y(x)^2+288 x^7 y(x)-144 x^7-216 x^6 y(x)^3-216 x^6 y(x)^2-288 x^6 y(x)-456 x^6+864 x^5 y(x)^2+1008 x^5 y(x)-576 x^5-648 x^4 y(x)^3-972 x^4 y(x)^2-216 x^4 y(x)-864 x^4+432 x^3 y(x)^2+720 x^3 y(x)-756 x^3-648 x^2 y(x)^3-1296 x^2 y(x)^2-594 x^2 y(x)-1134 x^2-216 y(x)^3-540 y(x)^2-378 y(x)-432 x-513\right )}{216 \left (x^2+1\right )^4} \] ✓ Mathematica : cpu = 0.191033 (sec), leaf count = 143
\[\text {Solve}\left [174 \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {\left (\frac {x^3}{\left (x^2+1\right )^3}\right )^{2/3} \left (x^2+1\right ) \left (-4 x^3+6 x^2 y(x)+2 x^2+6 y(x)+5\right )}{2 \sqrt [3]{29} x^2}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]+18 c_1+\frac {29^{2/3} x \log \left (x^2+1\right )}{\sqrt [3]{\frac {x^3}{\left (x^2+1\right )^3}} \left (x^2+1\right )}=0,y(x)\right ]\]
✓ Maple : cpu = 0.115 (sec), leaf count = 91
\[ \left \{ y \left ( x \right ) ={\frac {58\,{\it RootOf} \left ( -162\,\int ^{{\it \_Z}}\! \left ( 841\,{{\it \_a}}^{3}-27\,{\it \_a}+27 \right ) ^{-1}{d{\it \_a}}+\ln \left ( {x}^{2}+1 \right ) +6\,{\it \_C1} \right ) {x}^{2}+12\,{x}^{3}-6\,{x}^{2}+58\,{\it RootOf} \left ( -162\,\int ^{{\it \_Z}}\! \left ( 841\,{{\it \_a}}^{3}-27\,{\it \_a}+27 \right ) ^{-1}{d{\it \_a}}+\ln \left ( {x}^{2}+1 \right ) +6\,{\it \_C1} \right ) -15}{18\,{x}^{2}+18}} \right \} \]