\[ y'(x)=-\frac {x \left (64 x^9-288 x^8 y(x)-96 x^8+432 x^7 y(x)^2+288 x^7 y(x)-144 x^7-216 x^6 y(x)^3-216 x^6 y(x)^2-288 x^6 y(x)-456 x^6+864 x^5 y(x)^2+1008 x^5 y(x)-576 x^5-648 x^4 y(x)^3-972 x^4 y(x)^2-216 x^4 y(x)-864 x^4+432 x^3 y(x)^2+720 x^3 y(x)-756 x^3-648 x^2 y(x)^3-1296 x^2 y(x)^2-594 x^2 y(x)-1134 x^2-216 y(x)^3-540 y(x)^2-378 y(x)-432 x-513\right )}{216 \left (x^2+1\right )^4} \] ✓ Mathematica : cpu = 0.524111 (sec), leaf count = 151
DSolve[Derivative[1][y][x] == -1/216*(x*(-513 - 432*x - 1134*x^2 - 756*x^3 - 864*x^4 - 576*x^5 - 456*x^6 - 144*x^7 - 96*x^8 + 64*x^9 - 378*y[x] - 594*x^2*y[x] + 720*x^3*y[x] - 216*x^4*y[x] + 1008*x^5*y[x] - 288*x^6*y[x] + 288*x^7*y[x] - 288*x^8*y[x] - 540*y[x]^2 - 1296*x^2*y[x]^2 + 432*x^3*y[x]^2 - 972*x^4*y[x]^2 + 864*x^5*y[x]^2 - 216*x^6*y[x]^2 + 432*x^7*y[x]^2 - 216*y[x]^3 - 648*x^2*y[x]^3 - 648*x^4*y[x]^3 - 216*x^6*y[x]^3))/(1 + x^2)^4,y[x],x]
\[\text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {\frac {3 x y(x)}{x^2+1}+\frac {-4 x^4+2 x^3+5 x}{2 \left (x^2+1\right )^2}}{\sqrt [3]{29} \sqrt [3]{\frac {x^3}{\left (x^2+1\right )^3}}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=\frac {29^{2/3} \left (\frac {x^3}{\left (x^2+1\right )^3}\right )^{2/3} \left (x^2+1\right )^2 \log \left (x^2+1\right )}{18 x^2}+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.078 (sec), leaf count = 91
dsolve(diff(y(x),x) = -1/216*x/(x^2+1)^4*(-513-432*x-216*y(x)^3-540*y(x)^2-378*y(x)-864*x^4-1134*x^2+720*x^3*y(x)-594*x^2*y(x)-288*y(x)*x^8+288*y(x)*x^7-648*y(x)^3*x^4-288*y(x)*x^6+864*y(x)^2*x^5-216*y(x)*x^4-144*x^7+64*x^9-96*x^8+432*y(x)^2*x^7+1008*x^5*y(x)-216*x^6*y(x)^3-1296*x^2*y(x)^2-648*x^2*y(x)^3+432*x^3*y(x)^2-972*x^4*y(x)^2-216*x^6*y(x)^2-456*x^6-576*x^5-756*x^3),y(x))
\[y \left (x \right ) = \frac {58 \RootOf \left (-162 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+\ln \left (x^{2}+1\right )+6 c_{1}\right ) x^{2}+12 x^{3}-6 x^{2}+58 \RootOf \left (-162 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+\ln \left (x^{2}+1\right )+6 c_{1}\right )-15}{18 x^{2}+18}\]