2.304   ODE No. 304

\[ 5 x^2 y(x)^3+\left (10 x^3 y(x)^2+x^2 y(x)+2 x\right ) y'(x)+x y(x)^2=0 \] Mathematica : cpu = 0.420414 (sec), leaf count = 44


\[\text {Solve}\left [y(x) \sqrt {5 x^2 y(x)^2+2} e^{\frac {\tan ^{-1}\left (\sqrt {\frac {5}{2}} x y(x)\right )}{\sqrt {10}}}=c_1,y(x)\right ]\] Maple : cpu = 0.251 (sec), leaf count = 44


\[y \relax (x ) = \frac {\tan \left (\RootOf \left (\sqrt {10}\, \ln \left (\frac {4 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) \left (\tan ^{2}\left (\textit {\_Z} \right )+1\right )}{5 x^{2}}\right )+2 \sqrt {10}\, c_{1}+2 \textit {\_Z} \right )\right ) \sqrt {10}}{5 x}\]