23.1.608 problem 602

Internal problem ID [5215]
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 : 602
Date solved : Tuesday, September 30, 2025 at 11:56:00 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 16

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

\[ y = \sqrt {\frac {1}{\operatorname {LambertW}\left (c_1 \,x^{2}\right )}}\, x \]

✓ Mathematica. Time used: 5.498 (sec). Leaf size: 49

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

\begin{align*} y(x)&\to -\frac {x}{\sqrt {W\left (e^{-2 c_1} x^2\right )}}\\ y(x)&\to \frac {x}{\sqrt {W\left (e^{-2 c_1} x^2\right )}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.698 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = e^{C_{1} + \frac {W\left (x^{2} e^{- 2 C_{1}}\right )}{2}} \]