2.781   ODE No. 781

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

\[ y'(x)=\frac {y(x) \left (x^4+x^3+3 y(x)^2+x\right )}{x \left (6 y(x)^2+x\right )} \] Mathematica : cpu = 0.473437 (sec), leaf count = 82

\[\left \{\left \{y(x)\to -\frac {\sqrt {x} \sqrt {W\left (6 x e^{\frac {2 x^3}{3}+x^2+2 c_1}\right )}}{\sqrt {6}}\right \},\left \{y(x)\to \frac {\sqrt {x} \sqrt {W\left (6 x e^{\frac {2 x^3}{3}+x^2+2 c_1}\right )}}{\sqrt {6}}\right \}\right \}\] Maple : cpu = 1.228 (sec), leaf count = 61

\[ \left \{ \left ( \left ( y \left ( x \right ) \right ) ^{-2}+6\,{x}^{-1} \right ) ^{-1}={\frac {x}{54} \left ( {{\rm e}^{{\it RootOf} \left ( 2\,{x}^{3}{{\rm e}^{{\it \_Z}}}+3\,{{\rm e}^{{\it \_Z}}}{x}^{2}-3\,{{\rm e}^{{\it \_Z}}}\ln \left ( 1/2\,{\frac {{{\rm e}^{{\it \_Z}}}+9}{x}} \right ) +9\,{{\rm e}^{{\it \_Z}}}{\it \_C1}+3\,{\it \_Z}\,{{\rm e}^{{\it \_Z}}}+27 \right ) }}+9 \right ) } \right \} \]