23.1.119 problem 122

Internal problem ID [4726]
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 : 122
Date solved : Tuesday, September 30, 2025 at 08:19:58 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+\sin \left (2 x \right ) \csc \left (2 y\right )&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

ode:=diff(y(x),x)+sin(2*x)*csc(2*y(x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\arccos \left (-\cos \left (2 x \right )+4 c_1 \right )}{2} \]

✓ Mathematica. Time used: 0.172 (sec). Leaf size: 37

ode=D[y[x],x]+Sin[2*x]*Csc[2*y[x]]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\sin (2 K[1])dK[1]\&\right ]\left [\int _1^x-\sin (2 K[2])dK[2]+c_1\right ] \end{align*}

✓ Sympy. Time used: 0.285 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(sin(2*x)/sin(2*y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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