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 = 1.1076 (sec), leaf count = 78

\[\text {Solve}\left [-i a e^x=\frac {2 e^{\frac {1}{2} \left (-i a e^x-\frac {i}{y(x)}\right )^2}}{2 c_1+\sqrt {2 \pi } \text {erfi}\left (\frac {-i a e^x-\frac {i}{y(x)}}{\sqrt {2}}\right )},y(x)\right ]\] Maple : cpu = 0.112 (sec), leaf count = 50

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