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 = 0.363933 (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 = 0.136 (sec), leaf count = 54

\[ \left \{ {\it \_C1}-{\frac {{\frac {i}{3}}}{x}{{\rm e}^{{\frac { \left ( 3\,xy \left ( x \right ) -1 \right ) ^{2}}{2\, \left ( y \left ( x \right ) \right ) ^{2}}}}}}+{\frac {\sqrt {\pi }\sqrt {2}}{2}{\it Erf} \left ( {\frac { \left ( -i+3\,iy \left ( x \right ) x \right ) \sqrt {2}}{2\,y \left ( x \right ) }} \right ) }=0 \right \} \]