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]
\[ \boxed {y^{\prime }-\frac {\cot \left (t \right ) y}{1+y}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 9
dsolve(diff(y(t),t) = cot(t)*y(t)/(1+y(t)),y(t), singsol=all)
\[ y \left (t \right ) = \operatorname {LambertW}\left (c_{1} \sin \left (t \right )\right ) \]
✓ Solution by Mathematica
Time used: 1.602 (sec). Leaf size: 18
DSolve[y'[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*}