23.1.744 problem 747

Internal problem ID [5351]
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 : 747
Date solved : Tuesday, September 30, 2025 at 12:35:11 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.053 (sec). Leaf size: 18

ode:=x*(x-y(x)*tan(y(x)/x))*diff(y(x),x)+(x+y(x)*tan(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: 0.216 (sec). Leaf size: 31

ode=x(x-y[x]*Tan[y[x]/x])*D[y[x],x]+(x+y[x]*Tan[y[x]/x])*y[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 - y(x)*tan(y(x)/x))*Derivative(y(x), x) + (x + y(x)*tan(y(x)/x))*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

RecursionError : maximum recursion depth exceeded