60.7.15 problem 1605 (6.15)

Internal problem ID [11604]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1605 (6.15)
Date solved : Monday, January 27, 2025 at 11:24:42 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+a \,{\mathrm e}^{x} \sqrt {y}&=0 \end{align*}

✗ Solution by Maple

dsolve(diff(diff(y(x),x),x)+a*exp(x)*y(x)^(1/2)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[a*E^x*Sqrt[y[x]] + D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved