23.1.175 problem 175

Internal problem ID [4782]
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 : 175
Date solved : Tuesday, September 30, 2025 at 08:35:59 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y^{\prime }+\left (1-x y\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

ode:=x*diff(y(x),x)+(1-x*y(x))*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{\left (-\ln \left (x \right )+c_1 \right ) x} \]

✓ Mathematica. Time used: 0.093 (sec). Leaf size: 22

ode=x*D[y[x],x]+(1-x*y[x])*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{-x \log (x)+c_1 x}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.113 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) + (-x*y(x) + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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