83.3.4 problem 1 (d)

Internal problem ID [21923]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter III. First order differential equations of the first degree. Ex. IV at page 38
Problem number : 1 (d)
Date solved : Thursday, October 02, 2025 at 08:09:50 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 31

ode:=diff(y(x),x) = y(x)/x-csc(y(x)/x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {x \sin \left (\frac {2 y}{x}\right )-2 y}{4 x}-\ln \left (x \right )-c_1 = 0 \]

✓ Mathematica. Time used: 0.194 (sec). Leaf size: 33

ode=D[y[x],x]==y[x]/x - Csc[ y[x]/x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {y(x)}{2 x}-\frac {1}{4} \sin \left (\frac {2 y(x)}{x}\right )=-\log (x)+c_1,y(x)\right ] \]

✗ Sympy

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

TypeError : cannot determine truth value of Relational: 2*x < -4*x/(exp(2*_X0*I/x) + 2*exp(_X0*I/x)