2.37   ODE No. 37

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

\[ -a e^x y(x)^2+y'(x)-y(x)^3=0 \] Mathematica : cpu = 1.05781 (sec), leaf count = 78

\[\text {Solve}\left [-i a e^x=\frac {2 e^{\frac {1}{2} \left (-i a e^x-\frac {i}{y(x)}\right )^2}}{\sqrt {2 \pi } \text {erfi}\left (\frac {-i a e^x-\frac {i}{y(x)}}{\sqrt {2}}\right )+2 c_1},y(x)\right ]\] Maple : cpu = 0.095 (sec), leaf count = 50

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