\[ y'(x)=\frac {x \left (x^2+y(x)^2+1\right )}{x^6+3 x^4 y(x)^2+3 x^2 y(x)^4-x^2 y(x)+y(x)^6-y(x)^3-y(x)} \] ✓ Mathematica : cpu = 0.137126 (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 = 0.284 (sec), leaf count = 37
\[-\frac {1}{4 \left (y \relax (x )^{2}+x^{2}\right )^{2}}-\frac {1}{2 y \relax (x )^{2}+2 x^{2}}-y \relax (x )+c_{1} = 0\]