Internal problem ID [10417]
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: 16-b(vi).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {t \cot \left (x\right ) x^{\prime }+2=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 10
dsolve(t*cot(x(t))*diff(x(t),t)=-2,x(t), singsol=all)
\[ x \left (t \right ) = \arcsin \left (\frac {c_{1}}{t^{2}}\right ) \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 14
DSolve[t*Cot[x[t]]*x'[t]==-2,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \arcsin \left (\frac {e^{c_1}}{t^2}\right ) \\ \end{align*}