60.1.357 problem 364

Internal problem ID [10371]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 364
Date solved : Sunday, March 30, 2025 at 04:30:24 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.133 (sec). Leaf size: 18

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

\[ y = x \operatorname {RootOf}\left (\textit {\_Z} \cos \left (\textit {\_Z} \right ) x^{2}-c_1 \right ) \]

✓ Mathematica. Time used: 0.328 (sec). Leaf size: 31

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

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

✗ Sympy

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

Timed Out