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]
Solve \begin {gather*} \boxed {\cos \relax (y) \sin \relax (t ) y^{\prime }-\cos \relax (t ) \sin \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.088 (sec). Leaf size: 9
dsolve(cos(y(t))*sin(t)*diff(y(t),t) = cos(t)*sin(y(t)),y(t), singsol=all)
\[ y \relax (t ) = \arcsin \left (c_{1} \sin \relax (t )\right ) \]
✓ Solution by Mathematica
Time used: 1.188 (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 \text {ArcSin}\left (\frac {1}{2} c_1 \sin (t)\right ) \\ y(t)\to 0 \\ \end{align*}