Internal problem ID [4186]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\cos \relax (y) \sin \relax (x )-\cos \relax (x ) \sin \relax (y) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.25 (sec). Leaf size: 11
dsolve(sin(x)*cos(y(x))=cos(x)*sin(y(x))*diff(y(x),x),y(x), singsol=all)
\[ y \relax (x ) = \arccos \left (\frac {\cos \relax (x )}{c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 6.365 (sec). Leaf size: 47
DSolve[Sin[x]*Cos[y[x]]==Cos[x]*Sin[y[x]]*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\text {ArcCos}\left (\frac {1}{2} c_1 \cos (x)\right ) \\ y(x)\to \text {ArcCos}\left (\frac {1}{2} c_1 \cos (x)\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}