72.2.24 problem 19 a(i)

Internal problem ID [14659]
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(i)
Date solved : Tuesday, January 28, 2025 at 06:46:43 AM
CAS classification : [_quadrature]

\begin{align*} \theta ^{\prime }&=\frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 21

dsolve(diff(theta(t),t)=1-cos(theta(t))+(1+cos(theta(t)))*(-1/10),theta(t), singsol=all)
 

\[ \theta \left (t \right ) = -2 \arctan \left (\frac {\tanh \left (\frac {\left (t +c_{1} \right ) \sqrt {10}}{10}\right ) \sqrt {10}}{10}\right ) \]

✓ Solution by Mathematica

Time used: 0.217 (sec). Leaf size: 50

DSolve[D[ theta[t],t]==1-Cos[theta[t]]+(1+Cos[theta[t]])*(-1/10),theta[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} \theta (t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{11 \cos (K[1])-9}dK[1]\&\right ]\left [-\frac {t}{10}+c_1\right ] \\ \theta (t)\to -\arccos \left (\frac {9}{11}\right ) \\ \theta (t)\to \arccos \left (\frac {9}{11}\right ) \\ \end{align*}