Internal problem ID [12648]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {w^{\prime }-\left (1-w\right ) \sin \left (w\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(diff(w(t),t)=(1-w(t))*sin( w(t)),w(t), singsol=all)
\[ t +\int _{}^{w \left (t \right )}\frac {1}{\left (-1+\textit {\_a} \right ) \sin \left (\textit {\_a} \right )}d \textit {\_a} +c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 12.825 (sec). Leaf size: 41
DSolve[w'[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*}