72.5.14 problem 4 and 16(i)

Internal problem ID [14700]
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 and 16(i)
Date solved : Tuesday, January 28, 2025 at 07:11:54 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} w \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 5

dsolve([diff(w(t),t)=w(t)*cos( w(t)),w(0) = 0],w(t), singsol=all)
 

\[ w = 0 \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 6

DSolve[{D[w[t],t]==w[t]*Cos[ w[t]],{w[0]==0}},w[t],t,IncludeSingularSolutions -> True]
 

\[ w(t)\to 0 \]