72.2.25 problem 19 a(ii)

Internal problem ID [14581]
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 1.3 page 47
Problem number : 19 a(ii)
Date solved : Thursday, March 13, 2025 at 03:37:10 AM
CAS classification : [_quadrature]

\begin{align*} \theta ^{\prime }&=2 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 9

ode:=diff(theta(t),t) = 2; 
dsolve(ode,theta(t), singsol=all);
 

\[ \theta \left (t \right ) = 2 t +c_{1} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 11

ode=D[ theta[t],t]==1-Cos[theta[t]]+(1+Cos[theta[t]]); 
ic={}; 
DSolve[{ode,ic},theta[t],t,IncludeSingularSolutions->True]
 

\[ \theta (t)\to 2 t+c_1 \]

✓ Sympy. Time used: 0.045 (sec). Leaf size: 7

from sympy import * 
t = symbols("t") 
theta = Function("theta") 
ode = Eq(Derivative(theta(t), t) - 2,0) 
ics = {} 
dsolve(ode,func=theta(t),ics=ics)
 

\[ \theta {\left (t \right )} = C_{1} + 2 t \]