81.3.20 problem 20

Internal problem ID [18638]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 20
Date solved : Tuesday, January 28, 2025 at 12:05:13 PM
CAS classification : [_separable]

\begin{align*} \sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 9

dsolve((sin(x)*cos(y(x))) +(cos(x)*sin(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 5.870 (sec). Leaf size: 47

DSolve[(Sin[x]*Cos[y[x]]) +(Cos[x]*Sin[y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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