79.1.15 problem 3 (iii)

Internal problem ID [18502]
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 : Tuesday, January 28, 2025 at 11:51:12 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[D[x[t],t]==Cos[x[t]/t],x[t],t,IncludeSingularSolutions -> True]
 

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