\[ a e^x \sqrt {y(x)}+y''(x)=0 \] ✗ Mathematica : cpu = 20.1664 (sec), leaf count = 0
DSolve[a*E^x*Sqrt[y[x]] + Derivative[2][y][x] == 0,y[x],x]
, could not solve
DSolve[a*E^x*Sqrt[y[x]] + Derivative[2][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0
dsolve(diff(diff(y(x),x),x)+a*exp(x)*y(x)^(1/2)=0,y(x))
, result contains DESol or ODESolStruc
\[y \left (x \right ) = \left (\textit {\_a} \,{\mathrm e}^{\int 2 \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +2 c_{1}}\right )\boldsymbol {\mathrm {where}}\left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=\left (a \sqrt {\textit {\_a}}+4 \textit {\_a} \right ) \textit {\_}b\left (\textit {\_a} \right )^{3}+4 \textit {\_}b\left (\textit {\_a} \right )^{2}\right \}, \left \{\textit {\_a} =y \left (x \right ) {\mathrm e}^{-2 x}, \textit {\_}b\left (\textit {\_a} \right )=\frac {{\mathrm e}^{2 x}}{\frac {d}{d x}y \left (x \right )-2 y \left (x \right )}\right \}, \left \{x =\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}, y \left (x \right )=\textit {\_a} \,{\mathrm e}^{\int 2 \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +2 c_{1}}\right \}\right ]\]