2.1605   ODE No. 1605

\[ a e^x \sqrt {y(x)}+y''(x)=0 \] Mathematica : cpu = 20.1664 (sec), leaf count = 0


, 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


, result contains DESol or ODESolStruc

\[y \relax (x ) = \left (\textit {\_a} \,{\mathrm e}^{\int 2 \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +2 c_{1}}\right )\boldsymbol {\mathrm {where}}\left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=\left (a \sqrt {\textit {\_a}}+4 \textit {\_a} \right ) \textit {\_}b\left (\textit {\_a} \right )^{3}+4 \textit {\_}b\left (\textit {\_a} \right )^{2}\right \}, \left \{\textit {\_a} =y \relax (x ) {\mathrm e}^{-2 x}, \textit {\_}b\left (\textit {\_a} \right )=\frac {{\mathrm e}^{2 x}}{\frac {d}{d x}y \relax (x )-2 y \relax (x )}\right \}, \left \{x =\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}, y \relax (x )=\textit {\_a} \,{\mathrm e}^{\int 2 \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +2 c_{1}}\right \}\right ]\]