30.6.10 problem 11

Internal problem ID [7545]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Review problems. page 79
Problem number : 11
Date solved : Tuesday, September 30, 2025 at 04:47:04 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 14

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

\[ x = t -\arctan \left (-t +c_1 \right ) \]

✓ Mathematica. Time used: 0.357 (sec). Leaf size: 31

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

\begin{align*} x(t)&\to t+\arctan \left (t+\frac {c_1}{2}\right )\\ x(t)&\to t+\arctan \left (t+\frac {c_1}{2}\right ) \end{align*}

✗ Sympy

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

Timed Out