23.1.208 problem 204

Internal problem ID [4815]
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 : 204
Date solved : Tuesday, September 30, 2025 at 08:42:28 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.259 (sec). Leaf size: 37

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

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

✗ Sympy

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

TypeError : cannot determine truth value of Relational: -1 < exp(2*_X0*I/x)