72.5.15 problem 4 and 16(ii)

Internal problem ID [14701]
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(ii)
Date solved : Tuesday, January 28, 2025 at 07:11:56 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} w \left (3\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 1.360 (sec). Leaf size: 20

dsolve([diff(w(t),t)=w(t)*cos( w(t)),w(3) = 1],w(t), singsol=all)
 

\[ w = \operatorname {RootOf}\left (\int _{\textit {\_Z}}^{1}\frac {\sec \left (\textit {\_a} \right )}{\textit {\_a}}d \textit {\_a} +t -3\right ) \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{D[w[t],t]==w[t]*Cos[ w[t]],{w[3]==1}},w[t],t,IncludeSingularSolutions -> True]
 

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