Internal problem ID [11410]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 1, First order differential equations. Section 1.4.1. Integrating factors. Exercises
page 41
Problem number: 1(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\cos \left (t \right ) x^{\prime }-2 x \sin \left (x\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(cos(t)*diff(x(t),t)-2*x(t)*sin(x(t))=0,x(t), singsol=all)
\[ \ln \left (\sec \left (t \right )+\tan \left (t \right )\right )-\left (\int _{}^{x \left (t \right )}\frac {1}{2 \textit {\_a} \sin \left (\textit {\_a} \right )}d \textit {\_a} \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 10.596 (sec). Leaf size: 40
DSolve[Cos[t]*x'[t]-2*x[t]*Sin[x[t]]==0,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\csc (K[1])}{K[1]}dK[1]\&\right ]\left [4 \text {arctanh}\left (\tan \left (\frac {t}{2}\right )\right )+c_1\right ] x(t)\to 0 \end{align*}