\[ y'(x)=\frac {x \left (x^2+y(x)^2+1\right )}{x^6+3 x^4 y(x)^2+3 x^2 y(x)^4-x^2 y(x)+y(x)^6-y(x)^3-y(x)} \] ✓ Mathematica : cpu = 0.0970673 (sec), leaf count = 326
DSolve[Derivative[1][y][x] == (x*(1 + x^2 + y[x]^2))/(x^6 - y[x] - x^2*y[x] + 3*x^4*y[x]^2 - y[x]^3 + 3*x^2*y[x]^4 + y[x]^6),y[x],x]
\[\left \{\left \{y(x)\to \text {Root}\left [4 \text {$\#$1}^5-4 \text {$\#$1}^4 c_1+8 \text {$\#$1}^3 x^2+\text {$\#$1}^2 \left (2-8 c_1 x^2\right )+4 \text {$\#$1} x^4-4 c_1 x^4+2 x^2+1\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [4 \text {$\#$1}^5-4 \text {$\#$1}^4 c_1+8 \text {$\#$1}^3 x^2+\text {$\#$1}^2 \left (2-8 c_1 x^2\right )+4 \text {$\#$1} x^4-4 c_1 x^4+2 x^2+1\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [4 \text {$\#$1}^5-4 \text {$\#$1}^4 c_1+8 \text {$\#$1}^3 x^2+\text {$\#$1}^2 \left (2-8 c_1 x^2\right )+4 \text {$\#$1} x^4-4 c_1 x^4+2 x^2+1\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [4 \text {$\#$1}^5-4 \text {$\#$1}^4 c_1+8 \text {$\#$1}^3 x^2+\text {$\#$1}^2 \left (2-8 c_1 x^2\right )+4 \text {$\#$1} x^4-4 c_1 x^4+2 x^2+1\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [4 \text {$\#$1}^5-4 \text {$\#$1}^4 c_1+8 \text {$\#$1}^3 x^2+\text {$\#$1}^2 \left (2-8 c_1 x^2\right )+4 \text {$\#$1} x^4-4 c_1 x^4+2 x^2+1\& ,5\right ]\right \}\right \}\] ✓ Maple : cpu = 0.197 (sec), leaf count = 37
dsolve(diff(y(x),x) = x*(x^2+y(x)^2+1)/(-y(x)^3-x^2*y(x)-y(x)+y(x)^6+3*y(x)^4*x^2+3*y(x)^2*x^4+x^6),y(x))
\[-\frac {1}{4 \left (y \left (x \right )^{2}+x^{2}\right )^{2}}-\frac {1}{2 y \left (x \right )^{2}+2 x^{2}}-y \left (x \right )+c_{1} = 0\]