\[ \left (x^2+y(x)^2\right ) y'(x)+2 x (y(x)+2 x)=0 \] ✓ Mathematica : cpu = 1.8182 (sec), leaf count = 372
\[\left \{\left \{y(x)\to \frac {\sqrt [3]{\sqrt {-8 e^{3 c_1} x^3+e^{6 c_1}+20 x^6}+e^{3 c_1}-4 x^3}}{\sqrt [3]{2}}-\frac {\sqrt [3]{2} x^2}{\sqrt [3]{\sqrt {-8 e^{3 c_1} x^3+e^{6 c_1}+20 x^6}+e^{3 c_1}-4 x^3}}\right \},\left \{y(x)\to \frac {i 2^{2/3} \left (\sqrt {3}+i\right ) \left (\sqrt {-8 e^{3 c_1} x^3+e^{6 c_1}+20 x^6}+e^{3 c_1}-4 x^3\right ){}^{2/3}+\sqrt [3]{2} \left (2+2 i \sqrt {3}\right ) x^2}{4 \sqrt [3]{\sqrt {-8 e^{3 c_1} x^3+e^{6 c_1}+20 x^6}+e^{3 c_1}-4 x^3}}\right \},\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) x^2}{2^{2/3} \sqrt [3]{\sqrt {-8 e^{3 c_1} x^3+e^{6 c_1}+20 x^6}+e^{3 c_1}-4 x^3}}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{\sqrt {-8 e^{3 c_1} x^3+e^{6 c_1}+20 x^6}+e^{3 c_1}-4 x^3}}{2 \sqrt [3]{2}}\right \}\right \}\]
✓ Maple : cpu = 0.222 (sec), leaf count = 352
\[ \left \{ y \left ( x \right ) ={1 \left ( {\frac {1}{2}\sqrt [3]{4-16\,{x}^{3}{{\it \_C1}}^{3/2}+4\,\sqrt {20\,{{\it \_C1}}^{3}{x}^{6}-8\,{x}^{3}{{\it \_C1}}^{3/2}+1}}}-2\,{\frac {{x}^{2}{\it \_C1}}{\sqrt [3]{4-16\,{x}^{3}{{\it \_C1}}^{3/2}+4\,\sqrt {20\,{{\it \_C1}}^{3}{x}^{6}-8\,{x}^{3}{{\it \_C1}}^{3/2}+1}}}} \right ) {\frac {1}{\sqrt {{\it \_C1}}}}},y \left ( x \right ) =-{\frac {1}{4} \left ( \left ( 4\,i{\it \_C1}\,{x}^{2}+i \left ( 4-16\,{x}^{3}{{\it \_C1}}^{3/2}+4\,\sqrt {20\,{{\it \_C1}}^{3}{x}^{6}-8\,{x}^{3}{{\it \_C1}}^{3/2}+1} \right ) ^{{\frac {2}{3}}} \right ) \sqrt {3}-4\,{x}^{2}{\it \_C1}+ \left ( 4-16\,{x}^{3}{{\it \_C1}}^{3/2}+4\,\sqrt {20\,{{\it \_C1}}^{3}{x}^{6}-8\,{x}^{3}{{\it \_C1}}^{3/2}+1} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{4-16\,{x}^{3}{{\it \_C1}}^{3/2}+4\,\sqrt {20\,{{\it \_C1}}^{3}{x}^{6}-8\,{x}^{3}{{\it \_C1}}^{3/2}+1}}}}{\frac {1}{\sqrt {{\it \_C1}}}}},y \left ( x \right ) ={\frac {1}{4} \left ( 4\,i\sqrt {3}{\it \_C1}\,{x}^{2}+i\sqrt {3} \left ( 4-16\,{x}^{3}{{\it \_C1}}^{3/2}+4\,\sqrt {20\,{{\it \_C1}}^{3}{x}^{6}-8\,{x}^{3}{{\it \_C1}}^{3/2}+1} \right ) ^{{\frac {2}{3}}}+4\,{x}^{2}{\it \_C1}- \left ( 4-16\,{x}^{3}{{\it \_C1}}^{3/2}+4\,\sqrt {20\,{{\it \_C1}}^{3}{x}^{6}-8\,{x}^{3}{{\it \_C1}}^{3/2}+1} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{4-16\,{x}^{3}{{\it \_C1}}^{3/2}+4\,\sqrt {20\,{{\it \_C1}}^{3}{x}^{6}-8\,{x}^{3}{{\it \_C1}}^{3/2}+1}}}}{\frac {1}{\sqrt {{\it \_C1}}}}} \right \} \]