\[ a y'(x)+b x e^{y(x)}+x y''(x)=0 \] ✗ Mathematica : cpu = 0.260383 (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 = 0. (sec), leaf count = 0
, result contains DESol or ODESolStruc
\[y \relax (x ) = \left (\textit {\_a} -2 \left (\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} \right )-2 c_{1}\right )\boldsymbol {\mathrm {where}}\left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=\left (b \,{\mathrm e}^{\textit {\_a}}-2 a +2\right ) \textit {\_}b\left (\textit {\_a} \right )^{3}+\left (a -1\right ) \textit {\_}b\left (\textit {\_a} \right )^{2}\right \}, \left \{\textit {\_a} =y \relax (x )+2 \ln \relax (x ), \textit {\_}b\left (\textit {\_a} \right )=\frac {1}{x \left (\frac {d}{d x}y \relax (x )\right )+2}\right \}, \left \{x ={\mathrm e}^{\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}}, y \relax (x )=\textit {\_a} -2 \left (\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} \right )-2 c_{1}\right \}\right ]\]