Internal problem ID [1672]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.4. Page 24
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\cos \left (y\right ) \sin \left (t \right ) y^{\prime }-\cos \left (t \right ) \sin \left (y\right )=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 9
dsolve(cos(y(t))*sin(t)*diff(y(t),t) = cos(t)*sin(y(t)),y(t), singsol=all)
\[ y \left (t \right ) = \arcsin \left (c_{1} \sin \left (t \right )\right ) \]
✓ Solution by Mathematica
Time used: 3.204 (sec). Leaf size: 19
DSolve[Cos[y[t]]*Sin[t]*y'[t] == Cos[t]*Sin[y[t]],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \arcsin \left (\frac {1}{2} c_1 \sin (t)\right ) y(t)\to 0 \end{align*}