\[ y'(x)=\frac {x^3 y(x)^6+x^3 y(x)^4+x^3+3 x^2 y(x)^4+2 x^2 y(x)^2+3 x y(x)^2+x+1}{x^5 y(x)} \] ✓ Mathematica : cpu = 0.185983 (sec), leaf count = 64
\[\text {Solve}\left [\frac {1}{2} \text {RootSum}\left [2 \text {$\#$1}^3+2 \text {$\#$1}^2+1\& ,\frac {\log \left (\frac {x y(x)^2+1}{x}-\text {$\#$1}\right )}{3 \text {$\#$1}^2+2 \text {$\#$1}}\& \right ]+\frac {1}{x}+c_1=0,y(x)\right ]\] ✓ Maple : cpu = 0.559 (sec), leaf count = 84
\[\left \{y \left (x \right ) = \frac {\sqrt {\left (x \RootOf \left (c_{1} x +x \left (\int _{}^{\textit {\_Z}}\frac {1}{2 \textit {\_a}^{3}+2 \textit {\_a}^{2}+1}d \textit {\_a} \right )+1\right )-1\right ) x}}{x}, y \left (x \right ) = -\frac {\sqrt {\left (x \RootOf \left (c_{1} x +x \left (\int _{}^{\textit {\_Z}}\frac {1}{2 \textit {\_a}^{3}+2 \textit {\_a}^{2}+1}d \textit {\_a} \right )+1\right )-1\right ) x}}{x}\right \}\]