60.1.342 problem 349

Internal problem ID [10356]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 349
Date solved : Sunday, March 30, 2025 at 04:23:25 PM
CAS classification : [[_homogeneous, `class A`]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 17

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

\[ y = \arcsin \left (\frac {1}{2 \ln \left (x \right )+2 c_1}\right ) x \]

✓ Mathematica. Time used: 0.482 (sec). Leaf size: 20

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

\begin{align*} y(x)\to x \csc ^{-1}(2 (\log (x)+c_1)) \\ y(x)\to 0 \\ \end{align*}

✗ Sympy

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

TypeError : cannot determine truth value of Relational