72.5.18 problem 5

Internal problem ID [14704]
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 : 5
Date solved : Tuesday, January 28, 2025 at 07:12:02 AM
CAS classification : [_quadrature]

\begin{align*} w^{\prime }&=\left (1-w\right ) \sin \left (w\right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve(diff(w(t),t)=(1-w(t))*sin( w(t)),w(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.238 (sec). Leaf size: 41

DSolve[D[w[t],t]==(1-w[t])*Sin[ w[t]],w[t],t,IncludeSingularSolutions -> True]
 

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