2.111   ODE No. 111

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

\[ x y'(x)+y(x)^3+3 x y(x)^2=0 \] Mathematica : cpu = 0.508279 (sec), leaf count = 55

\[\text {Solve}\left [-3 x=\frac {2 e^{\frac {1}{2} \left (\frac {1}{y(x)}-3 x\right )^2}}{\sqrt {2 \pi } \text {erfi}\left (\frac {\frac {1}{y(x)}-3 x}{\sqrt {2}}\right )+2 c_1},y(x)\right ]\] Maple : cpu = 0.128 (sec), leaf count = 54

\[\left \{c_{1}+\frac {\sqrt {2}\, \sqrt {\pi }\, \erf \left (\frac {\left (3 i x y \left (x \right )-i\right ) \sqrt {2}}{2 y \left (x \right )}\right )}{2}-\frac {i {\mathrm e}^{\frac {\left (3 x y \left (x \right )-1\right )^{2}}{2 y \left (x \right )^{2}}}}{3 x} = 0\right \}\]