\[ y'(x)=\frac {2 y(x)^8}{128 x^3 y(x)^6+32 x^2 y(x)^6+96 x^2 y(x)^4+2 y(x)^6+y(x)^5+16 x y(x)^4+24 x y(x)^2+2 y(x)^2+2} \] ✓ Mathematica : cpu = 0.489549 (sec), leaf count = 720
\[\text {Solve}\left [\int _1^{y(x)}\left (\text {RootSum}\left [64 \text {$\#$1}^3 K[1]^6+16 \text {$\#$1}^2 K[1]^6+K[1]^6+48 \text {$\#$1}^2 K[1]^4+8 \text {$\#$1} K[1]^4+12 \text {$\#$1} K[1]^2+K[1]^2+1\& ,\frac {\log (x-\text {$\#$1})}{48 \text {$\#$1}^2 K[1]^4+8 \text {$\#$1} K[1]^4+24 \text {$\#$1} K[1]^2+2 K[1]^2+3}\& \right ] K[1]^3+\frac {K[1]^3}{2 \left (64 x^3 K[1]^6+16 x^2 K[1]^6+K[1]^6+48 x^2 K[1]^4+8 x K[1]^4+12 x K[1]^2+K[1]^2+1\right )}-\frac {\text {RootSum}\left [64 \text {$\#$1}^3 K[1]^6+16 \text {$\#$1}^2 K[1]^6+K[1]^6+48 \text {$\#$1}^2 K[1]^4+8 \text {$\#$1} K[1]^4+12 \text {$\#$1} K[1]^2+K[1]^2+1\& ,\frac {128 x \log (x-\text {$\#$1}) \text {$\#$1}^2 K[1]^6+320 \log (x-\text {$\#$1}) \text {$\#$1}^2 K[1]^6-24 x \log (x-\text {$\#$1}) K[1]^6+2 \log (x-\text {$\#$1}) K[1]^6-288 x \log (x-\text {$\#$1}) \text {$\#$1} K[1]^6+24 \log (x-\text {$\#$1}) \text {$\#$1} K[1]^6+32 \log (x-\text {$\#$1}) \text {$\#$1}^2 K[1]^4+16 \text {$\#$1}^2 K[1]^4-72 x \log (x-\text {$\#$1}) K[1]^4+64 x \log (x-\text {$\#$1}) \text {$\#$1} K[1]^4+88 \log (x-\text {$\#$1}) \text {$\#$1} K[1]^4-36 \text {$\#$1} K[1]^4-3 K[1]^4+8 x \log (x-\text {$\#$1}) K[1]^2+2 \log (x-\text {$\#$1}) K[1]^2+16 \log (x-\text {$\#$1}) \text {$\#$1} K[1]^2+8 \text {$\#$1} K[1]^2-9 K[1]^2+2 \log (x-\text {$\#$1})+1}{64 x \text {$\#$1}^2 K[1]^6+160 \text {$\#$1}^2 K[1]^6+112 x K[1]^6-144 x \text {$\#$1} K[1]^6-112 \text {$\#$1} K[1]^6+K[1]^6+16 \text {$\#$1}^2 K[1]^4-36 x K[1]^4+32 x \text {$\#$1} K[1]^4+44 \text {$\#$1} K[1]^4+4 x K[1]^2+8 \text {$\#$1} K[1]^2+K[1]^2+1}\& \right ]}{2 K[1]}+\frac {1}{K[1]^2}\right )dK[1]-\frac {1}{4} y(x)^4 \text {RootSum}\left [64 \text {$\#$1}^3 y(x)^6+16 \text {$\#$1}^2 y(x)^6+48 \text {$\#$1}^2 y(x)^4+8 \text {$\#$1} y(x)^4+12 \text {$\#$1} y(x)^2+y(x)^6+y(x)^2+1\& ,\frac {\log (x-\text {$\#$1})}{48 \text {$\#$1}^2 y(x)^4+8 \text {$\#$1} y(x)^4+24 \text {$\#$1} y(x)^2+2 y(x)^2+3}\& \right ]=c_1,y(x)\right ]\] ✓ Maple : cpu = 1.171 (sec), leaf count = 41
\[x -\RootOf \left (\left (\int _{}^{\textit {\_Z}}\frac {1}{64 \textit {\_a}^{3}+16 \textit {\_a}^{2}+1}d \textit {\_a} \right ) y \relax (x )+c_{1} y \relax (x )+1\right )+\frac {1}{4 y \relax (x )^{2}} = 0\]