2.1605   ODE No. 1605

\[ a e^x \sqrt {y(x)}+y''(x)=0 \]

✗ Mathematica : cpu = 20.3012 (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

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