23.1.533 problem 523

Internal problem ID [5140]
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 : 523
Date solved : Tuesday, September 30, 2025 at 11:44:10 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 15

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

\[ y = -\operatorname {LambertW}\left (-\frac {{\mathrm e}^{x} c_1}{x}\right ) \]

✓ Mathematica. Time used: 0.071 (sec). Leaf size: 37

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

\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {K[1]-1}{K[1]}dK[1]\&\right ][-x+\log (x)+c_1]\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.187 (sec). Leaf size: 12

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

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