63.5.37 problem 16-b(vi)

Internal problem ID [13111]
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)
Date solved : Tuesday, January 28, 2025 at 04:53:05 AM
CAS classification : [_separable]

\begin{align*} t \cot \left (x\right ) x^{\prime }&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.053 (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: 0.068 (sec). Leaf size: 14

DSolve[t*Cot[x[t]]*D[x[t],t]==-2,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \arcsin \left (\frac {e^{c_1}}{t^2}\right ) \]