79.1.15 problem 3 (iii)

Internal problem ID [18423]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 3. Solutions of first-order equations. Exercises at page 47
Problem number : 3 (iii)
Date solved : Thursday, March 13, 2025 at 11:56:19 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 27

ode:=diff(x(t),t) = cos(x(t)/t); 
dsolve(ode,x(t), singsol=all);
 

\[ x = \operatorname {RootOf}\left (-\int _{}^{\textit {\_Z}}-\frac {1}{-\cos \left (\textit {\_a} \right )+\textit {\_a}}d \textit {\_a} +\ln \left (t \right )+c_{1} \right ) t \]

✓ Mathematica. Time used: 0.085 (sec). Leaf size: 33

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

\[ \text {Solve}\left [\int _1^{\frac {x(t)}{t}}\frac {1}{K[1]-\cos (K[1])}dK[1]=-\log (t)+c_1,x(t)\right ] \]

✓ Sympy. Time used: 1.630 (sec). Leaf size: 24

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

\[ x{\left (t \right )} = C_{1} e^{- \int \limits ^{\frac {t}{x{\left (t \right )}}} \frac {\cos {\left (\frac {1}{u_{1}} \right )}}{u_{1} \cos {\left (\frac {1}{u_{1}} \right )} - 1}\, du_{1}} \]