80.2.17 problem 24

Internal problem ID [21160]
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 2. Theory of first order differential equations. Excercise 2.6 at page 37
Problem number : 24
Date solved : Thursday, October 02, 2025 at 07:15:00 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} x^{\prime }&=\arctan \left (x\right )+t \end{align*}

✗ Maple

ode:=diff(x(t),t) = arctan(x(t))+t; 
dsolve(ode,x(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : The given ODE t - atan(x(t)) + Derivative(x(t), t) cannot be solved by the lie group method