23.1.633 problem 627

Internal problem ID [5240]
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 : 627
Date solved : Sunday, October 12, 2025 at 01:24:03 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} \left (\cot \left (x \right )-2 y^{2}\right ) y^{\prime }&=y^{3} \csc \left (x \right ) \sec \left (x \right ) \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 52

ode:=(cot(x)-2*y(x)^2)*diff(y(x),x) = y(x)^3*csc(x)*sec(x); 
dsolve(ode,y(x), singsol=all);
 

\[ -\frac {y^{2}}{2 \tan \left (x \right ) y^{2}-1} = -\frac {\left ({\mathrm e}^{\operatorname {RootOf}\left (-{\mathrm e}^{\textit {\_Z}} \ln \left (-\frac {i \left ({\mathrm e}^{\textit {\_Z}}+9\right ) \cot \left (x \right )}{2}\right )+3 c_1 \,{\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+9\right )}+9\right ) \cot \left (x \right )}{18} \]

✓ Mathematica. Time used: 3.387 (sec). Leaf size: 74

ode=(Cot[x]-2*y[x]^2)*D[y[x],x]==y[x]^3*Csc[x]*Sec[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {i \sqrt {\cot (x)} \sqrt {W\left (-2 e^{-8 c_1} \tan (x)\right )}}{\sqrt {2}}\\ y(x)&\to \frac {i \sqrt {\cot (x)} \sqrt {W\left (-2 e^{-8 c_1} \tan (x)\right )}}{\sqrt {2}}\\ y(x)&\to 0 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-2*y(x)**2 + 1/tan(x))*Derivative(y(x), x) - y(x)**3/(sin(x)*cos(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out