80.3.46 problem 49

Internal problem ID [21210]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 3. First order nonlinear differential equations. Excercise 3.7 at page 67
Problem number : 49
Date solved : Thursday, October 02, 2025 at 07:26:48 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} {x^{\prime }}^{2}&=x^{2}+t^{2}-1 \end{align*}

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=D[x[t],t]^2==x[t]^2+t^2-1; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-t**2 - x(t)**2 + Derivative(x(t), t)**2 + 1,0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

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