19.1.8 problem 8

Internal problem ID [3522]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.4, page 36
Problem number : 8
Date solved : Monday, January 27, 2025 at 07:40:25 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1 \end{align*}

✓ Solution by Maple

Time used: 0.208 (sec). Leaf size: 11

dsolve(diff(y(x),x)=(cos(x-y(x)))/(sin(x)*sin(y(x)))-1,y(x), singsol=all)
 

\[ y \left (x \right ) = \arccos \left (\frac {\csc \left (x \right )}{c_{1}}\right ) \]

✓ Solution by Mathematica

Time used: 5.880 (sec). Leaf size: 47

DSolve[D[y[x],x]==(Cos[x-y[x]])/(Sin[x]*Sin[y[x]])-1,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\arccos \left (-\frac {1}{2} c_1 \csc (x)\right ) \\ y(x)\to \arccos \left (-\frac {1}{2} c_1 \csc (x)\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}