2.1665   ODE No. 1665

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

\[ x y''(x)+2 y'(x)+x e^{y(x)}=0 \] Mathematica : cpu = 0.119726 (sec), leaf count = 0 , could not solve

DSolve[E^y[x]*x + 2*Derivative[1][y][x] + x*Derivative[2][y][x] == 0, y[x], x]

Maple : cpu = 0.552 (sec), leaf count = 84

\[\left \{y \left (x \right ) = \mathit {ODESolStruc} \left (-2 c_{1}+\textit {\_a} -2 \left (\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} \right ), \left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=\left ({\mathrm e}^{\textit {\_a}}-2\right ) \textit {\_}b\left (\textit {\_a} \right )^{3}+\textit {\_}b\left (\textit {\_a} \right )^{2}\right \}, \left \{\textit {\_a} =2 \ln \left (x \right )+y \left (x \right ), \textit {\_}b\left (\textit {\_a} \right )=\frac {1}{x \left (\frac {d}{d x}y \left (x \right )\right )+2}\right \}, \left \{x ={\mathrm e}^{c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}, y \left (x \right )=-2 c_{1}+\textit {\_a} -2 \left (\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} \right )\right \}\right ]\right )\right \}\]