2.304   ODE No. 304

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

\[ 5 x^2 y(x)^3+\left (10 x^3 y(x)^2+x^2 y(x)+2 x\right ) y'(x)+x y(x)^2=0 \] Mathematica : cpu = 0.482891 (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 = 0.256 (sec), leaf count = 44

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