Internal problem ID [523]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.4. Page 76
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\cot \relax (t ) y}{1+y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.042 (sec). Leaf size: 9
dsolve(diff(y(t),t) = cot(t)*y(t)/(1+y(t)),y(t), singsol=all)
\[ y \relax (t ) = \LambertW \left (c_{1} \sin \relax (t )\right ) \]
✓ Solution by Mathematica
Time used: 2.445 (sec). Leaf size: 18
DSolve[y'[t] == Cot[t]*y[t]/(1+y[t]),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \text {ProductLog}\left (e^{c_1} \sin (t)\right ) \\ y(t)\to 0 \\ \end{align*}