72.3.13 problem 17

Internal problem ID [14677]
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 1.4 page 61
Problem number : 17
Date solved : Tuesday, January 28, 2025 at 06:47:26 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} \theta \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.659 (sec). Leaf size: 29

dsolve([diff(theta(t),t)=1-cos( theta(t)) + (1+cos(theta(t)))*(-1/10),theta(0) = 1],theta(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 36

DSolve[{D[ theta[t],t]==1-Cos[ theta[t]] + (1+Cos[theta[t]])*(-1/10),{theta[0]==1}},theta[t],t,IncludeSingularSolutions -> True]
 

\[ \theta (t)\to -2 \arctan \left (\frac {\tanh \left (\frac {t}{\sqrt {10}}-\text {arctanh}\left (\sqrt {10} \tan \left (\frac {1}{2}\right )\right )\right )}{\sqrt {10}}\right ) \]