\[ \left (a+x^2+y(x)^2\right ) y'(x)+b+x^2+2 x y(x)=0 \] ✓ Mathematica : cpu = 0.201124 (sec), leaf count = 411
\[\left \{\left \{y(x)\to \frac {\sqrt [3]{\sqrt {2916 \left (a+x^2\right )^3+\left (-81 b x-27 x^3+81 c_1\right ){}^2}-81 b x-27 x^3+81 c_1}}{3 \sqrt [3]{2}}-\frac {3 \sqrt [3]{2} \left (a+x^2\right )}{\sqrt [3]{\sqrt {2916 \left (a+x^2\right )^3+\left (-81 b x-27 x^3+81 c_1\right ){}^2}-81 b x-27 x^3+81 c_1}}\right \},\left \{y(x)\to \frac {3 \left (1+i \sqrt {3}\right ) \left (a+x^2\right )}{2^{2/3} \sqrt [3]{\sqrt {2916 \left (a+x^2\right )^3+\left (-81 b x-27 x^3+81 c_1\right ){}^2}-81 b x-27 x^3+81 c_1}}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{\sqrt {2916 \left (a+x^2\right )^3+\left (-81 b x-27 x^3+81 c_1\right ){}^2}-81 b x-27 x^3+81 c_1}}{6 \sqrt [3]{2}}\right \},\left \{y(x)\to \frac {3 \left (1-i \sqrt {3}\right ) \left (a+x^2\right )}{2^{2/3} \sqrt [3]{\sqrt {2916 \left (a+x^2\right )^3+\left (-81 b x-27 x^3+81 c_1\right ){}^2}-81 b x-27 x^3+81 c_1}}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{\sqrt {2916 \left (a+x^2\right )^3+\left (-81 b x-27 x^3+81 c_1\right ){}^2}-81 b x-27 x^3+81 c_1}}{6 \sqrt [3]{2}}\right \}\right \}\] ✓ Maple : cpu = 0.039 (sec), leaf count = 657
\[\left \{y \left (x \right ) = \frac {-4 x^{2}-4 a +\left (-4 x^{3}-12 b x -12 c_{1}+4 \sqrt {5 x^{6}+6 c_{1} x^{3}+\left (12 a +6 b \right ) x^{4}+18 c_{1} b x +4 a^{3}+9 c_{1}^{2}+\left (12 a^{2}+9 b^{2}\right ) x^{2}}\right )^{\frac {2}{3}}}{2 \left (-4 x^{3}-12 b x -12 c_{1}+4 \sqrt {5 x^{6}+6 c_{1} x^{3}+\left (12 a +6 b \right ) x^{4}+18 c_{1} b x +4 a^{3}+9 c_{1}^{2}+\left (12 a^{2}+9 b^{2}\right ) x^{2}}\right )^{\frac {1}{3}}}, y \left (x \right ) = \frac {4 x^{2}+4 a +\left (4 i x^{2}+4 i a +i \left (-4 x^{3}-12 b x -12 c_{1}+4 \sqrt {5 x^{6}+6 c_{1} x^{3}+\left (12 a +6 b \right ) x^{4}+18 c_{1} b x +4 a^{3}+9 c_{1}^{2}+\left (12 a^{2}+9 b^{2}\right ) x^{2}}\right )^{\frac {2}{3}}\right ) \sqrt {3}-\left (-4 x^{3}-12 b x -12 c_{1}+4 \sqrt {5 x^{6}+6 c_{1} x^{3}+\left (12 a +6 b \right ) x^{4}+18 c_{1} b x +4 a^{3}+9 c_{1}^{2}+\left (12 a^{2}+9 b^{2}\right ) x^{2}}\right )^{\frac {2}{3}}}{4 \left (-4 x^{3}-12 b x -12 c_{1}+4 \sqrt {5 x^{6}+6 c_{1} x^{3}+\left (12 a +6 b \right ) x^{4}+18 c_{1} b x +4 a^{3}+9 c_{1}^{2}+\left (12 a^{2}+9 b^{2}\right ) x^{2}}\right )^{\frac {1}{3}}}, y \left (x \right ) = -\frac {-4 x^{2}-4 a +\left (4 i x^{2}+4 i a +i \left (-4 x^{3}-12 b x -12 c_{1}+4 \sqrt {5 x^{6}+6 c_{1} x^{3}+\left (12 a +6 b \right ) x^{4}+18 c_{1} b x +4 a^{3}+9 c_{1}^{2}+\left (12 a^{2}+9 b^{2}\right ) x^{2}}\right )^{\frac {2}{3}}\right ) \sqrt {3}+\left (-4 x^{3}-12 b x -12 c_{1}+4 \sqrt {5 x^{6}+6 c_{1} x^{3}+\left (12 a +6 b \right ) x^{4}+18 c_{1} b x +4 a^{3}+9 c_{1}^{2}+\left (12 a^{2}+9 b^{2}\right ) x^{2}}\right )^{\frac {2}{3}}}{4 \left (-4 x^{3}-12 b x -12 c_{1}+4 \sqrt {5 x^{6}+6 c_{1} x^{3}+\left (12 a +6 b \right ) x^{4}+18 c_{1} b x +4 a^{3}+9 c_{1}^{2}+\left (12 a^{2}+9 b^{2}\right ) x^{2}}\right )^{\frac {1}{3}}}\right \}\]