60.7.207 problem 1833 (book 6.242)

Internal problem ID [11757]
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 : Wednesday, March 05, 2025 at 03:05:51 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-a*exp(2*x) + y(x)*Derivative(y(x), (x, 2))**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve -a*exp(2*x) + y(x)*Derivative(y(x), (x, 2))**2