31.1.5 problem 1.5

Internal problem ID [5703]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 2
Problem number : 1.5
Date solved : Monday, January 27, 2025 at 01:08:24 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: 0.367 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 5.317 (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 \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*}