\[ \boxed { {x}^{7}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2\, \left ( {x}^{2}+1 \right ) \left ( y \left ( x \right ) \right ) ^{3}+5\,{x}^{3} \left ( y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 0.375548 (sec), leaf count = 123 \[ \text {Solve}\left [c_1=\frac {\frac {1}{2} \sqrt [4]{1-\left (\frac {i x^2}{y(x)}+\frac {i}{x}\right )^2} \left (\frac {i x^2}{y(x)}+\frac {i}{x}\right ) \, _2F_1\left (\frac {1}{2},\frac {5}{4};\frac {3}{2};\left (\frac {i x^2}{y(x)}+\frac {i}{x}\right )^2\right )+i x}{\sqrt [4]{-1+\left (\frac {i x^2}{y(x)}+\frac {i}{x}\right )^2}},y(x)\right ] \]
Maple: cpu = 0.031 (sec), leaf count = 63 \[ \left \{ {\it \_C1}+{x{\frac {1}{\sqrt [4]{ \left ( {x}^{-1}+{\frac {{x }^{2}}{y \left ( x \right ) }} \right ) ^{2}+1}}}}+{\frac {{x}^{3}+y \left ( x \right ) }{2\,xy \left ( x \right ) } {\mbox {$_2$F$_1$}({\frac {1}{2}},{\frac {5}{4}};\,{\frac {3}{2}};\,-{\frac { \left ( {x}^{3}+y \left ( x \right ) \right ) ^{2}}{{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}}})} }=0 \right \} \]