\[ \left (a+x^2+y(x)^2\right ) y'(x)+2 x y(x)=0 \] ✓ Mathematica : cpu = 0.17482 (sec), leaf count = 297
\[\left \{\left \{y(x)\to \frac {\sqrt [3]{\sqrt {2916 \left (a+x^2\right )^3+6561 c_1{}^2}+81 c_1}}{3 \sqrt [3]{2}}-\frac {3 \sqrt [3]{2} \left (a+x^2\right )}{\sqrt [3]{\sqrt {2916 \left (a+x^2\right )^3+6561 c_1{}^2}+81 c_1}}\right \},\left \{y(x)\to \frac {3 \left (1+i \sqrt {3}\right ) \left (a+x^2\right )}{2^{2/3} \sqrt [3]{\sqrt {2916 \left (a+x^2\right )^3+6561 c_1{}^2}+81 c_1}}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{\sqrt {2916 \left (a+x^2\right )^3+6561 c_1{}^2}+81 c_1}}{6 \sqrt [3]{2}}\right \},\left \{y(x)\to \frac {3 \left (1-i \sqrt {3}\right ) \left (a+x^2\right )}{2^{2/3} \sqrt [3]{\sqrt {2916 \left (a+x^2\right )^3+6561 c_1{}^2}+81 c_1}}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{\sqrt {2916 \left (a+x^2\right )^3+6561 c_1{}^2}+81 c_1}}{6 \sqrt [3]{2}}\right \}\right \}\] ✓ Maple : cpu = 0.027 (sec), leaf count = 401
\[y \relax (x ) = \frac {\left (-12 c_{1}+4 \sqrt {4 x^{6}+12 a \,x^{4}+12 a^{2} x^{2}+4 a^{3}+9 c_{1}^{2}}\right )^{\frac {2}{3}}-4 x^{2}-4 a}{2 \left (-12 c_{1}+4 \sqrt {4 x^{6}+12 a \,x^{4}+12 a^{2} x^{2}+4 a^{3}+9 c_{1}^{2}}\right )^{\frac {1}{3}}}\]