3.304   ODE No. 304

\[ \boxed { \left ( 10\,{x}^{3} \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}y \left ( x \right ) +2\,x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +5\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{3}+x \left ( y \left ( x \right ) \right ) ^{2}=0} \]

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

Mathematica: cpu = 45.176237 (sec), leaf count = 59 \[ \text {Solve}\left [-y(x) \left (\frac {\log \left (5 x^2 y(x)^2+2\right )}{2 y(x)}+\frac {\tan ^{-1}\left (\sqrt {\frac {5}{2}} x y(x)\right )}{\sqrt {10} y(x)}\right )-\log (y(x))=c_1,y(x)\right ] \]

Maple: cpu = 0.156 (sec), leaf count = 44 \[ \left \{ y \left ( x \right ) ={\frac {\sqrt {10}}{5\,x}\tan \left ( { \it RootOf} \left ( \sqrt {10}\ln \left ( {\frac {4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2} \left ( \left ( \tan \left ( { \it \_Z} \right ) \right ) ^{2}+1 \right ) }{5\,{x}^{2}}} \right ) +2\, \sqrt {10}{\it \_C1}+2\,{\it \_Z} \right ) \right ) } \right \} \]