Internal problem ID [12603]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {\theta ^{\prime }+\frac {11 \cos \left (\theta \right )}{10}={\frac {9}{10}}} \]
✓ Solution by Maple
Time used: 0.015 (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: 1.026 (sec). Leaf size: 69
DSolve[theta'[t]==1-Cos[theta[t]]+(1+Cos[theta[t]])*(-1/10),theta[t],t,IncludeSingularSolutions -> True]
\begin{align*} \theta (t)\to -2 \arctan \left (\frac {\tanh \left (\frac {t-10 c_1}{\sqrt {10}}\right )}{\sqrt {10}}\right ) \theta (t)\to -\arccos \left (\frac {9}{11}\right ) \theta (t)\to \arccos \left (\frac {9}{11}\right ) \theta (t)\to -2 \arctan \left (\frac {1}{\sqrt {10}}\right ) \theta (t)\to 2 \arctan \left (\frac {1}{\sqrt {10}}\right ) \end{align*}