2.728   ODE No. 728

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

\[ y'(x)=\frac {y(x) \left (x^3+3 y(x)^2\right )}{x \left (6 y(x)^2+x\right )} \] Mathematica : cpu = 0.350053 (sec), leaf count = 72

\[\left \{\left \{y(x)\to -\frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{x^2+2 c_1}}{x}\right )}}{\sqrt {6}}\right \},\left \{y(x)\to \frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{x^2+2 c_1}}{x}\right )}}{\sqrt {6}}\right \}\right \}\] Maple : cpu = 1.191 (sec), leaf count = 50

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