23.1.29 problem 24

Internal problem ID [4636]
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 : 24
Date solved : Tuesday, September 30, 2025 at 07:37:42 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=2 \csc \left (2 x \right ) \left (1-\tan \left (x \right )^{2}+y\right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

ode:=diff(y(x),x) = 2*csc(2*x)*(1-tan(x)^2+y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\sin \left (2 x \right ) c_1 -2}{\cos \left (2 x \right )+1} \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 17

ode=D[y[x],x]==2*Csc[2*x]*(1-Tan[x]^2+y[x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \tan (x) (-2 \csc (2 x)+c_1) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*(y(x) - tan(x)**2 + 1)*csc(2*x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out