2.1666   ODE No. 1666

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

\[ a y'(x)+b x e^{y(x)}+x y''(x)=0 \] Mathematica : cpu = 0.291787 (sec), leaf count = 0 , could not solve

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

Maple : cpu = 1.038 (sec), leaf count = 93

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