72.5.13 problem 4

Internal problem ID [14620]
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
Date solved : Thursday, March 13, 2025 at 04:10:20 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

ode:=diff(w(t),t) = w(t)*cos(w(t)); 
dsolve(ode,w(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.236 (sec). Leaf size: 50

ode=D[w[t],t]==w[t]*Cos[ w[t]]; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.366 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
w = Function("w") 
ode = Eq(-w(t)*cos(w(t)) + Derivative(w(t), t),0) 
ics = {} 
dsolve(ode,func=w(t),ics=ics)
 

\[ \int \limits ^{w{\left (t \right )}} \frac {1}{y \cos {\left (y \right )}}\, dy = C_{1} + t \]