72.5.13 problem 4

Internal problem ID [14699]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.6 page 89
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 07:11:53 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(diff(w(t),t)=w(t)*cos( w(t)),w(t), singsol=all)
 

\[ t -\int _{}^{w}\frac {\sec \left (\textit {\_a} \right )}{\textit {\_a}}d \textit {\_a} +c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.236 (sec). Leaf size: 50

DSolve[D[w[t],t]==w[t]*Cos[ w[t]],w[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} w(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\sec (K[1])}{K[1]}dK[1]\&\right ][t+c_1] \\ w(t)\to 0 \\ w(t)\to -\frac {\pi }{2} \\ w(t)\to \frac {\pi }{2} \\ \end{align*}