29.7.25 problem 200

Internal problem ID [4800]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 200
Date solved : Sunday, March 30, 2025 at 03:58:25 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 12

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

\[ y = -2 \arctan \left (\ln \left (x \right )+c_1 \right ) x \]

✓ Mathematica. Time used: 0.352 (sec). Leaf size: 31

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

\begin{align*} y(x)\to 2 x \arctan (-\log (x)+c_1) \\ y(x)\to -\pi x \\ y(x)\to \pi x \\ \end{align*}

✓ Sympy. Time used: 0.911 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = 2 x \operatorname {atan}{\left (C_{1} - \log {\left (x \right )} \right )} \]