29.5.4 problem 119

Internal problem ID [4721]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 5
Problem number : 119
Date solved : Tuesday, March 04, 2025 at 07:10:32 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 17

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

\[ y \left (x \right ) = \frac {\arccos \left (-\cos \left (2 x \right )+4 c_{1} \right )}{2} \]

✓ Mathematica. Time used: 0.581 (sec). Leaf size: 41

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 -\frac {1}{2} \arccos (-\cos (2 x)-2 c_1) \\ y(x)\to \frac {1}{2} \arccos (-\cos (2 x)-2 c_1) \\ \end{align*}

✓ Sympy. Time used: 0.421 (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)
 

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