23.1.531 problem 521

Internal problem ID [5138]
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 : 521
Date solved : Tuesday, September 30, 2025 at 11:44:06 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: 14

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

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

✓ Mathematica. Time used: 2.036 (sec). Leaf size: 21

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

✓ Sympy. Time used: 0.159 (sec). Leaf size: 10

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

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