\[ \boxed { \left ( \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}+a \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2\,xy \left ( x \right ) =0} \]
Mathematica: cpu = 0.014002 (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 = 0.015 (sec), leaf count = 470 \[ \left \{ y \left ( x \right ) ={\frac {1}{2}\sqrt [3]{-12\,{\it \_C1}+4 \,\sqrt {4\,{x}^{6}+12\,a{x}^{4}+12\,{a}^{2}{x}^{2}+4\,{a}^{3}+9\,{{ \it \_C1}}^{2}}}}-2\,{\frac {{x}^{2}+a}{\sqrt [3]{-12\,{\it \_C1}+4\, \sqrt {4\,{x}^{6}+12\,a{x}^{4}+12\,{a}^{2}{x}^{2}+4\,{a}^{3}+9\,{{\it \_C1}}^{2}}}}},y \left ( x \right ) =-{\frac {1}{4}\sqrt [3]{-12\,{\it \_C1}+4\,\sqrt {4\,{x}^{6}+12\,a{x}^{4}+12\,{a}^{2}{x}^{2}+4\,{a}^{3}+ 9\,{{\it \_C1}}^{2}}}}+{({x}^{2}+a){\frac {1}{\sqrt [3]{-12\,{\it \_C1 }+4\,\sqrt {4\,{x}^{6}+12\,a{x}^{4}+12\,{a}^{2}{x}^{2}+4\,{a}^{3}+9\,{ {\it \_C1}}^{2}}}}}}-{\frac {i}{2}}\sqrt {3} \left ( {\frac {1}{2} \sqrt [3]{-12\,{\it \_C1}+4\,\sqrt {4\,{x}^{6}+12\,a{x}^{4}+12\,{a}^{2 }{x}^{2}+4\,{a}^{3}+9\,{{\it \_C1}}^{2}}}}+2\,{\frac {{x}^{2}+a}{ \sqrt [3]{-12\,{\it \_C1}+4\,\sqrt {4\,{x}^{6}+12\,a{x}^{4}+12\,{a}^{2 }{x}^{2}+4\,{a}^{3}+9\,{{\it \_C1}}^{2}}}}} \right ) ,y \left ( x \right ) =-{\frac {1}{4}\sqrt [3]{-12\,{\it \_C1}+4\,\sqrt {4\,{x}^{6} +12\,a{x}^{4}+12\,{a}^{2}{x}^{2}+4\,{a}^{3}+9\,{{\it \_C1}}^{2}}}}+{({ x}^{2}+a){\frac {1}{\sqrt [3]{-12\,{\it \_C1}+4\,\sqrt {4\,{x}^{6}+12 \,a{x}^{4}+12\,{a}^{2}{x}^{2}+4\,{a}^{3}+9\,{{\it \_C1}}^{2}}}}}}+{ \frac {i}{2}}\sqrt {3} \left ( {\frac {1}{2}\sqrt [3]{-12\,{\it \_C1}+4 \,\sqrt {4\,{x}^{6}+12\,a{x}^{4}+12\,{a}^{2}{x}^{2}+4\,{a}^{3}+9\,{{ \it \_C1}}^{2}}}}+2\,{\frac {{x}^{2}+a}{\sqrt [3]{-12\,{\it \_C1}+4\, \sqrt {4\,{x}^{6}+12\,a{x}^{4}+12\,{a}^{2}{x}^{2}+4\,{a}^{3}+9\,{{\it \_C1}}^{2}}}}} \right ) \right \} \]