2.304   ODE No. 304

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

\[ \left (10 x^3 y(x)^2+x^2 y(x)+2 x\right ) y'(x)+5 x^2 y(x)^3+x y(x)^2=0 \] Mathematica : cpu = 0.338503 (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 = 0.207 (sec), leaf count = 44

\[ \left \{ y \left ( x \right ) ={\frac {\sqrt {10}}{5\,x}\tan \left ( {\it RootOf} \left ( \sqrt {10}\ln \left ( {\frac {4\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2} \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+1 \right ) }{5\,{x}^{2}}} \right ) +2\,\sqrt {10}{\it \_C1}+2\,{\it \_Z} \right ) \right ) } \right \} \]