Internal problem ID [12621]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {\theta ^{\prime }+\frac {11 \cos \left (\theta \right )}{10}={\frac {9}{10}}} \] With initial conditions \begin {align*} [\theta \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.11 (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: 0.061 (sec). Leaf size: 36
DSolve[{theta'[t]==1-Cos[ theta[t]] + (1+Cos[theta[t]])*(-1/10),{theta[0]==1}},theta[t],t,IncludeSingularSolutions -> True]
\[ \theta (t)\to -2 \arctan \left (\frac {\tanh \left (\frac {t}{\sqrt {10}}-\text {arctanh}\left (\sqrt {10} \tan \left (\frac {1}{2}\right )\right )\right )}{\sqrt {10}}\right ) \]