\[ y'(x)=-\frac {x \left (-288 x^8 y(x)+432 x^7 y(x)^2+288 x^7 y(x)-216 x^6 y(x)^3-216 x^6 y(x)^2-288 x^6 y(x)+864 x^5 y(x)^2+1008 x^5 y(x)-648 x^4 y(x)^3-972 x^4 y(x)^2-216 x^4 y(x)+432 x^3 y(x)^2+720 x^3 y(x)-648 x^2 y(x)^3-1296 x^2 y(x)^2-594 x^2 y(x)+64 x^9-96 x^8-144 x^7-456 x^6-576 x^5-864 x^4-756 x^3-1134 x^2-216 y(x)^3-540 y(x)^2-378 y(x)-432 x-513\right )}{216 \left (x^2+1\right )^4} \] ✓ Mathematica : cpu = 0.486708 (sec), leaf count = 151
\[\text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {\frac {3 x y(x)}{x^2+1}+\frac {-4 x^4+2 x^3+5 x}{2 \left (x^2+1\right )^2}}{\sqrt [3]{29} \sqrt [3]{\frac {x^3}{\left (x^2+1\right )^3}}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=\frac {29^{2/3} \left (\frac {x^3}{\left (x^2+1\right )^3}\right )^{2/3} \left (x^2+1\right )^2 \log \left (x^2+1\right )}{18 x^2}+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.236 (sec), leaf count = 91
\[ \left \{ y \left ( x \right ) ={\frac {58\,{\it RootOf} \left ( -162\,\int ^{{\it \_Z}}\! \left ( 841\,{{\it \_a}}^{3}-27\,{\it \_a}+27 \right ) ^{-1}{d{\it \_a}}+\ln \left ( {x}^{2}+1 \right ) +6\,{\it \_C1} \right ) {x}^{2}+12\,{x}^{3}-6\,{x}^{2}+58\,{\it RootOf} \left ( -162\,\int ^{{\it \_Z}}\! \left ( 841\,{{\it \_a}}^{3}-27\,{\it \_a}+27 \right ) ^{-1}{d{\it \_a}}+\ln \left ( {x}^{2}+1 \right ) +6\,{\it \_C1} \right ) -15}{18\,{x}^{2}+18}} \right \} \]