Internal problem ID [12963]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {w^{\prime }-w \cos \left (w\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(diff(w(t),t)=w(t)*cos( w(t)),w(t), singsol=all)
\[ t -\left (\int _{}^{w \left (t \right )}\frac {\sec \left (\textit {\_a} \right )}{\textit {\_a}}d \textit {\_a} \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 7.857 (sec). Leaf size: 50
DSolve[w'[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*}