\[ y'(x)=\frac {x \left (x^2+y(x)^2+1\right )}{x^6+3 x^4 y(x)^2+3 x^2 y(x)^4-x^2 y(x)+y(x)^6-y(x)^3-y(x)} \] ✓ Mathematica : cpu = 0.160783 (sec), leaf count = 326
\[\left \{\left \{y(x)\to \text {Root}\left [4 \text {$\#$1}^5-4 \text {$\#$1}^4 c_1+8 \text {$\#$1}^3 x^2+\text {$\#$1}^2 \left (2-8 c_1 x^2\right )+4 \text {$\#$1} x^4-4 c_1 x^4+2 x^2+1\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [4 \text {$\#$1}^5-4 \text {$\#$1}^4 c_1+8 \text {$\#$1}^3 x^2+\text {$\#$1}^2 \left (2-8 c_1 x^2\right )+4 \text {$\#$1} x^4-4 c_1 x^4+2 x^2+1\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [4 \text {$\#$1}^5-4 \text {$\#$1}^4 c_1+8 \text {$\#$1}^3 x^2+\text {$\#$1}^2 \left (2-8 c_1 x^2\right )+4 \text {$\#$1} x^4-4 c_1 x^4+2 x^2+1\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [4 \text {$\#$1}^5-4 \text {$\#$1}^4 c_1+8 \text {$\#$1}^3 x^2+\text {$\#$1}^2 \left (2-8 c_1 x^2\right )+4 \text {$\#$1} x^4-4 c_1 x^4+2 x^2+1\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [4 \text {$\#$1}^5-4 \text {$\#$1}^4 c_1+8 \text {$\#$1}^3 x^2+\text {$\#$1}^2 \left (2-8 c_1 x^2\right )+4 \text {$\#$1} x^4-4 c_1 x^4+2 x^2+1\& ,5\right ]\right \}\right \}\] ✓ Maple : cpu = 0.298 (sec), leaf count = 37
\[\left \{c_{1}-y \left (x \right )-\frac {1}{2 x^{2}+2 y \left (x \right )^{2}}-\frac {1}{4 \left (x^{2}+y \left (x \right )^{2}\right )^{2}} = 0\right \}\]