23.1.118 problem 121

Internal problem ID [4725]
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 : 121
Date solved : Tuesday, September 30, 2025 at 08:19:56 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.041 (sec). Leaf size: 9

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

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

✓ Mathematica. Time used: 0.088 (sec). Leaf size: 82

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

\[ \text {Solve}\left [\int _1^x(-\sin (K[1]-y(x))-\sin (K[1]+y(x)))dK[1]+\int _1^{y(x)}\left (\sin (x-K[2])-\sin (x+K[2])-\int _1^x(\cos (K[1]-K[2])-\cos (K[1]+K[2]))dK[1]\right )dK[2]=c_1,y(x)\right ] \]

✓ Sympy. Time used: 0.265 (sec). Leaf size: 20

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

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