38.1.7 problem 8

Internal problem ID [8168]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 8
Date solved : Tuesday, September 30, 2025 at 05:17:33 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }-\left (1-\frac {{x^{\prime }}^{2}}{3}\right ) x^{\prime }+x&=0 \end{align*}

✗ Maple

ode:=diff(diff(x(t),t),t)-(1-1/3*diff(x(t),t)^2)*diff(x(t),t)+x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[x[t],{t,2}]-(1-D[x[t],t]^2/3)*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((Derivative(x(t), t)**2/3 - 1)*Derivative(x(t), t) + x(t) + Derivative(x(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

NotImplementedError : The given ODE (sqrt((81*x(t) + 81*Derivative(x(t), (t, 2)))**2 - 2916)/2 + 81*x(t)/2 + 81*Derivative(x(t), (t, 2))/2)**(1/3)/3 + Derivative(x(t), t) + 3/(sqrt((81*x(t) + 81*Derivative(x(t), (t, 2)))**2 - 2916)/2 + 81*x(t)/2 + 81*Derivative(x(t), (t, 2))/2)**(1/3) cannot be solved by the factorable group method