\[ y'(x)=\frac {x \left (x^2+y(x)^2+1\right )}{3 x^4 y(x)^2+3 x^2 y(x)^4-x^2 y(x)+x^6+y(x)^6-y(x)^3-y(x)} \] ✓ Mathematica : cpu = 0.121226 (sec), leaf count = 326
\[\left \{\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^3 x^2+\text {$\#$1}^2 \left (2-8 c_1 x^2\right )+4 \text {$\#$1}^5-4 \text {$\#$1}^4 c_1+4 \text {$\#$1} x^4+2 x^2-4 c_1 x^4+1\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^3 x^2+\text {$\#$1}^2 \left (2-8 c_1 x^2\right )+4 \text {$\#$1}^5-4 \text {$\#$1}^4 c_1+4 \text {$\#$1} x^4+2 x^2-4 c_1 x^4+1\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^3 x^2+\text {$\#$1}^2 \left (2-8 c_1 x^2\right )+4 \text {$\#$1}^5-4 \text {$\#$1}^4 c_1+4 \text {$\#$1} x^4+2 x^2-4 c_1 x^4+1\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^3 x^2+\text {$\#$1}^2 \left (2-8 c_1 x^2\right )+4 \text {$\#$1}^5-4 \text {$\#$1}^4 c_1+4 \text {$\#$1} x^4+2 x^2-4 c_1 x^4+1\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^3 x^2+\text {$\#$1}^2 \left (2-8 c_1 x^2\right )+4 \text {$\#$1}^5-4 \text {$\#$1}^4 c_1+4 \text {$\#$1} x^4+2 x^2-4 c_1 x^4+1\& ,5\right ]\right \}\right \}\] ✓ Maple : cpu = 0.323 (sec), leaf count = 37
\[ \left \{ -{\frac {1}{4\, \left ( \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2} \right ) ^{2}}}- \left ( 2\, \left ( y \left ( x \right ) \right ) ^{2}+2\,{x}^{2} \right ) ^{-1}-y \left ( x \right ) +{\it \_C1}=0 \right \} \]