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 = 0.87792 (sec), leaf count = 73

\[\text {Solve}\left [-i a e^x=\frac {2 e^{-\frac {\left (a e^x y(x)+1\right )^2}{2 y(x)^2}}}{2 c_1-i \sqrt {2 \pi } \text {erf}\left (\frac {a e^x y(x)+1}{\sqrt {2} y(x)}\right )},y(x)\right ]\]

Maple : cpu = 0.096 (sec), leaf count = 50

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