\[ \left (a+x^2+y(x)^2\right ) y'(x)+b+x^2+2 x y(x)=0 \] ✓ Mathematica : cpu = 0.0359814 (sec), leaf count = 396
\[\left \{\left \{y(x)\to \frac {\sqrt [3]{2} \left (\sqrt {4 \left (a+x^2\right )^3+\left (3 b x-3 c_1+x^3\right ){}^2}-3 b x+3 c_1-x^3\right ){}^{2/3}-2 a-2 x^2}{2^{2/3} \sqrt [3]{\sqrt {4 \left (a+x^2\right )^3+\left (3 b x-3 c_1+x^3\right ){}^2}-3 b x+3 c_1-x^3}}\right \},\left \{y(x)\to \frac {\left (1+i \sqrt {3}\right ) \left (a+x^2\right )}{2^{2/3} \sqrt [3]{\sqrt {4 \left (a+x^2\right )^3+\left (3 b x-3 c_1+x^3\right ){}^2}-3 b x+3 c_1-x^3}}+\frac {i \left (\sqrt {3}+i\right ) \sqrt [3]{\sqrt {4 \left (a+x^2\right )^3+\left (3 b x-3 c_1+x^3\right ){}^2}-3 b x+3 c_1-x^3}}{2 \sqrt [3]{2}}\right \},\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) \left (a+x^2\right )}{2^{2/3} \sqrt [3]{\sqrt {4 \left (a+x^2\right )^3+\left (3 b x-3 c_1+x^3\right ){}^2}-3 b x+3 c_1-x^3}}-\frac {i \left (\sqrt {3}-i\right ) \sqrt [3]{\sqrt {4 \left (a+x^2\right )^3+\left (3 b x-3 c_1+x^3\right ){}^2}-3 b x+3 c_1-x^3}}{2 \sqrt [3]{2}}\right \}\right \}\]
✓ Maple : cpu = 0.031 (sec), leaf count = 657
\[ \left \{ y \left ( x \right ) ={\frac {1}{2} \left ( \left ( -4\,{x}^{3}-12\,bx-12\,{\it \_C1}+4\,\sqrt {5\,{x}^{6}+ \left ( 12\,a+6\,b \right ) {x}^{4}+6\,{x}^{3}{\it \_C1}+ \left ( 12\,{a}^{2}+9\,{b}^{2} \right ) {x}^{2}+18\,bx{\it \_C1}+4\,{a}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}-4\,{x}^{2}-4\,a \right ) {\frac {1}{\sqrt [3]{-4\,{x}^{3}-12\,bx-12\,{\it \_C1}+4\,\sqrt {5\,{x}^{6}+ \left ( 12\,a+6\,b \right ) {x}^{4}+6\,{x}^{3}{\it \_C1}+ \left ( 12\,{a}^{2}+9\,{b}^{2} \right ) {x}^{2}+18\,bx{\it \_C1}+4\,{a}^{3}+9\,{{\it \_C1}}^{2}}}}}},y \left ( x \right ) ={\frac {1}{4} \left ( \left ( i \left ( -4\,{x}^{3}-12\,bx-12\,{\it \_C1}+4\,\sqrt {5\,{x}^{6}+ \left ( 12\,a+6\,b \right ) {x}^{4}+6\,{x}^{3}{\it \_C1}+ \left ( 12\,{a}^{2}+9\,{b}^{2} \right ) {x}^{2}+18\,bx{\it \_C1}+4\,{a}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}+4\,i{x}^{2}+4\,ia \right ) \sqrt {3}- \left ( -4\,{x}^{3}-12\,bx-12\,{\it \_C1}+4\,\sqrt {5\,{x}^{6}+ \left ( 12\,a+6\,b \right ) {x}^{4}+6\,{x}^{3}{\it \_C1}+ \left ( 12\,{a}^{2}+9\,{b}^{2} \right ) {x}^{2}+18\,bx{\it \_C1}+4\,{a}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}+4\,{x}^{2}+4\,a \right ) {\frac {1}{\sqrt [3]{-4\,{x}^{3}-12\,bx-12\,{\it \_C1}+4\,\sqrt {5\,{x}^{6}+ \left ( 12\,a+6\,b \right ) {x}^{4}+6\,{x}^{3}{\it \_C1}+ \left ( 12\,{a}^{2}+9\,{b}^{2} \right ) {x}^{2}+18\,bx{\it \_C1}+4\,{a}^{3}+9\,{{\it \_C1}}^{2}}}}}},y \left ( x \right ) =-{\frac {1}{4} \left ( \left ( i \left ( -4\,{x}^{3}-12\,bx-12\,{\it \_C1}+4\,\sqrt {5\,{x}^{6}+ \left ( 12\,a+6\,b \right ) {x}^{4}+6\,{x}^{3}{\it \_C1}+ \left ( 12\,{a}^{2}+9\,{b}^{2} \right ) {x}^{2}+18\,bx{\it \_C1}+4\,{a}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}+4\,i{x}^{2}+4\,ia \right ) \sqrt {3}+ \left ( -4\,{x}^{3}-12\,bx-12\,{\it \_C1}+4\,\sqrt {5\,{x}^{6}+ \left ( 12\,a+6\,b \right ) {x}^{4}+6\,{x}^{3}{\it \_C1}+ \left ( 12\,{a}^{2}+9\,{b}^{2} \right ) {x}^{2}+18\,bx{\it \_C1}+4\,{a}^{3}+9\,{{\it \_C1}}^{2}} \right ) ^{{\frac {2}{3}}}-4\,{x}^{2}-4\,a \right ) {\frac {1}{\sqrt [3]{-4\,{x}^{3}-12\,bx-12\,{\it \_C1}+4\,\sqrt {5\,{x}^{6}+ \left ( 12\,a+6\,b \right ) {x}^{4}+6\,{x}^{3}{\it \_C1}+ \left ( 12\,{a}^{2}+9\,{b}^{2} \right ) {x}^{2}+18\,bx{\it \_C1}+4\,{a}^{3}+9\,{{\it \_C1}}^{2}}}}}} \right \} \]