10.3.8 problem 12

Internal problem ID [1173]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.4. Page 76
Problem number : 12
Date solved : Monday, January 27, 2025 at 04:39:17 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.370 (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: 1.440 (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*}