\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-{\frac {x \left ( -513-432\,x-594\,{x}^{2}y \left ( x \right ) +720\,{x}^{3}y \left ( x \right ) -378\,y \left ( x \right ) -864\,{x}^{4}-756\,{x}^{3}-1134\,{x}^{2}-540\, \left ( y \left ( x \right ) \right ) ^{2}-216\, \left ( y \left ( x \right ) \right ) ^{3}-972\,{x}^{4} \left ( y \left ( x \right ) \right ) ^{2}-216\,{x}^{6} \left ( y \left ( x \right ) \right ) ^{2}+432\,{x}^{3} \left ( y \left ( x \right ) \right ) ^{2}-648\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{3}-1296\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}-288\,y \left ( x \right ) {x}^{8}+288\,y \left ( x \right ) {x}^{7}+864\, \left ( y \left ( x \right ) \right ) ^{2}{x}^{5}-648\, \left ( y \left ( x \right ) \right ) ^{3}{x}^{4}-144\,{x}^{7}+64\,{x}^{9}-96\,{x}^{8}-288\,y \left ( x \right ) {x}^{6}-216\,y \left ( x \right ) {x}^{4}+432\, \left ( y \left ( x \right ) \right ) ^{2}{x}^{7}-216\,{x}^{6} \left ( y \left ( x \right ) \right ) ^{3}+1008\,{x}^{5}y \left ( x \right ) -456\,{x}^{6}-576\,{x}^{5} \right ) }{216\, \left ( {x}^{2}+1 \right ) ^{4}}}=0} \]
Mathematica: cpu = 0.128516 (sec), leaf count = 151 \[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {\frac {3 x y(x)}{x^2+1}+\frac {-4 x^4+2 x^3+5 x}{2 \left (x^2+1\right )^2}}{\sqrt [3]{29} \sqrt [3]{\frac {x^3}{\left (x^2+1\right )^3}}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=c_1+\frac {29^{2/3} \left (\frac {x^3}{\left (x^2+1\right )^3}\right )^{2/3} \left (x^2+1\right )^2 \log \left (x^2+1\right )}{18 x^2},y(x)\right ] \]
Maple: cpu = 0.062 (sec), leaf count = 90 \[ \left \{ y \left ( x \right ) ={\frac {58\,{\it RootOf} \left ( -162\, \int ^{{\it \_Z}}\! \left ( 841\,{{\it \_a}}^{3}-27\,{\it \_a}+27 \right ) ^{-1}{d{\it \_a}}+\ln \left ( {x}^{2}+1 \right ) +6\,{\it \_C1 } \right ) {x}^{2}+12\,{x}^{3}-6\,{x}^{2}+58\,{\it RootOf} \left ( -162 \,\int ^{{\it \_Z}}\! \left ( 841\,{{\it \_a}}^{3}-27\,{\it \_a}+27 \right ) ^{-1}{d{\it \_a}}+\ln \left ( {x}^{2}+1 \right ) +6\,{\it \_C1 } \right ) -15}{18\,{x}^{2}+18}} \right \} \]