34.2.8 problem 8

Internal problem ID [6038]
Book : A treatise on ordinary and partial differential equations by William Woolsey Johnson. 1913
Section : Chapter 2, Equations of the first order and degree. page 20
Problem number : 8
Date solved : Monday, January 27, 2025 at 01:34:10 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 11

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

\[ y = \arccos \left (\frac {\cos \left (x \right )}{c_1}\right ) \]

✓ Solution by Mathematica

Time used: 5.273 (sec). Leaf size: 47

DSolve[Sin[x]*Cos[y[x]]==Cos[x]*Sin[y[x]]*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

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