75.21.7 problem 702

Internal problem ID [17097]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 16. The method of isoclines for differential equations of the second order. Exercises page 158
Problem number : 702
Date solved : Thursday, March 13, 2025 at 09:15:46 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+{\mathrm e}^{-x^{\prime }}-x&=0 \end{align*}

✗ Maple

ode:=diff(diff(x(t),t),t)+exp(-diff(x(t),t))-x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[x[t],{t,2}]+Exp[-D[x[t],t]]-x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

NotImplementedError : The given ODE -log(-1/(-x(t) + Derivative(x(t), (t, 2)))) + Derivative(x(t), t) cannot be solved by the factorable group method