76.3.12 problem 12

Internal problem ID [17383]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.4 (Differences between linear and nonlinear equations). Problems at page 79
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 10:03:55 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {\cot \left (t \right ) y}{1+y} \end{align*}

✓ Solution by Maple

Time used: 0.687 (sec). Leaf size: 9

dsolve(diff(y(t),t)=cot(t)*y(t)/(1+y(t)),y(t), singsol=all)
 

\[ y = \operatorname {LambertW}\left (c_{1} \sin \left (t \right )\right ) \]

✓ Solution by Mathematica

Time used: 1.548 (sec). Leaf size: 18

DSolve[D[y[t],t]==Cot[t]*y[t]/(1+y[t]),y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to W\left (e^{c_1} \sin (t)\right ) \\ y(t)\to 0 \\ \end{align*}