Internal problem ID [929]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\sin \relax (x ) \sin \relax (y)+\cos \relax (y) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 12
dsolve(sin(x)*sin(y(x))+cos(y(x))*diff(y(x),x)= 0,y(x), singsol=all)
\[ y \relax (x ) = \arcsin \left (\frac {{\mathrm e}^{\cos \relax (x )}}{c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 21.992 (sec). Leaf size: 22
DSolve[Sin[x]*Sin[y[x]]+Cos[y[x]]*y'[x]== 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {ArcSin}\left (e^{\cos (x)+\frac {c_1}{2}}\right ) \\ y(x)\to 0 \\ \end{align*}