\[ \left (a+x^2+y(x)^2\right ) y'(x)+2 x y(x)=0 \] ✓ Mathematica : cpu = 0.0203065 (sec), leaf count = 294
\[\left \{\left \{y(x)\to \frac {\sqrt [3]{2} \left (\sqrt {4 \left (a+x^2\right )^3+9 c_1^2}+3 c_1\right ){}^{2/3}-2 a-2 x^2}{2^{2/3} \sqrt [3]{\sqrt {4 \left (a+x^2\right )^3+9 c_1^2}+3 c_1}}\right \},\left \{y(x)\to \frac {\left (1+i \sqrt {3}\right ) \left (a+x^2\right )}{2^{2/3} \sqrt [3]{\sqrt {4 \left (a+x^2\right )^3+9 c_1^2}+3 c_1}}+\frac {i \left (\sqrt {3}+i\right ) \sqrt [3]{\sqrt {4 \left (a+x^2\right )^3+9 c_1^2}+3 c_1}}{2 \sqrt [3]{2}}\right \},\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) \left (a+x^2\right )}{2^{2/3} \sqrt [3]{\sqrt {4 \left (a+x^2\right )^3+9 c_1^2}+3 c_1}}-\frac {i \left (\sqrt {3}-i\right ) \sqrt [3]{\sqrt {4 \left (a+x^2\right )^3+9 c_1^2}+3 c_1}}{2 \sqrt [3]{2}}\right \}\right \}\]
✓ Maple : cpu = 0.029 (sec), leaf count = 401
\[ \left \{ y \left ( x \right ) =-{\frac {1}{4} \left ( \left ( i \left ( -12\,{\it \_C1}+4\,\sqrt {4\,{x}^{6}+12\,a{x}^{4}+12\,{a}^{2}{x}^{2}+4\,{a}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}+4\,i{x}^{2}+4\,ia \right ) \sqrt {3}+ \left ( -12\,{\it \_C1}+4\,\sqrt {4\,{x}^{6}+12\,a{x}^{4}+12\,{a}^{2}{x}^{2}+4\,{a}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}-4\,{x}^{2}-4\,a \right ) {\frac {1}{\sqrt [3]{-12\,{\it \_C1}+4\,\sqrt {4\,{x}^{6}+12\,a{x}^{4}+12\,{a}^{2}{x}^{2}+4\,{a}^{3}+9\,{{\it \_C1}}^{2}}}}}},y \left ( x \right ) ={\frac {1}{2} \left ( \left ( -12\,{\it \_C1}+4\,\sqrt {4\,{x}^{6}+12\,a{x}^{4}+12\,{a}^{2}{x}^{2}+4\,{a}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}-4\,{x}^{2}-4\,a \right ) {\frac {1}{\sqrt [3]{-12\,{\it \_C1}+4\,\sqrt {4\,{x}^{6}+12\,a{x}^{4}+12\,{a}^{2}{x}^{2}+4\,{a}^{3}+9\,{{\it \_C1}}^{2}}}}}},y \left ( x \right ) ={\frac {1}{4} \left ( \left ( i \left ( -12\,{\it \_C1}+4\,\sqrt {4\,{x}^{6}+12\,a{x}^{4}+12\,{a}^{2}{x}^{2}+4\,{a}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}+4\,i{x}^{2}+4\,ia \right ) \sqrt {3}- \left ( -12\,{\it \_C1}+4\,\sqrt {4\,{x}^{6}+12\,a{x}^{4}+12\,{a}^{2}{x}^{2}+4\,{a}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}+4\,{x}^{2}+4\,a \right ) {\frac {1}{\sqrt [3]{-12\,{\it \_C1}+4\,\sqrt {4\,{x}^{6}+12\,a{x}^{4}+12\,{a}^{2}{x}^{2}+4\,{a}^{3}+9\,{{\it \_C1}}^{2}}}}}} \right \} \]