23.1.115 problem 118

Internal problem ID [4722]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 118
Date solved : Tuesday, September 30, 2025 at 08:19:48 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.038 (sec). Leaf size: 9

ode:=diff(y(x),x)+cot(x)*cot(y(x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \arccos \left (\sin \left (x \right ) c_1 \right ) \]

✓ Mathematica. Time used: 4.614 (sec). Leaf size: 47

ode=D[y[x],x]+Cot[x]*Cot[y[x]]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.243 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + 1/(tan(x)*tan(y(x))),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \operatorname {acos}{\left (C_{1} \sin {\left (x \right )} \right )} + 2 \pi , \ y{\left (x \right )} = \operatorname {acos}{\left (C_{1} \sin {\left (x \right )} \right )}\right ] \]