60.7.242 problem 1833 (book 6.242)

Internal problem ID [11831]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1833 (book 6.242)
Date solved : Monday, January 27, 2025 at 11:43:11 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y {y^{\prime \prime }}^{2}-a \,{\mathrm e}^{2 x}&=0 \end{align*}

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved