Internal problem ID [2120]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.4, Separable Differential Equations.
page 43
Problem number: Problem 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\cos \left (x -y\right )}{\sin \relax (x ) \sin \relax (y)}+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.115 (sec). Leaf size: 13
dsolve(diff(y(x),x)=cos(x-y(x))/(sin(x)*sin(y(x)))-1,y(x), singsol=all)
\[ y \relax (x ) = \arccos \left (\frac {1}{\sin \relax (x ) c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 1.89 (sec). Leaf size: 47
DSolve[y'[x]==Cos[x-y[x]]/(Sin[x]*Sin[y[x]])-1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\text {ArcCos}\left (-\frac {1}{2} c_1 \csc (x)\right ) \\ y(x)\to \text {ArcCos}\left (-\frac {1}{2} c_1 \csc (x)\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}