29.19.7 problem 520

Internal problem ID [5116]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 19
Problem number : 520
Date solved : Sunday, March 30, 2025 at 06:41:24 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: 3.76 (sec). Leaf size: 26

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 (-\frac {e^{x-c_1}}{x}\right ) \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.321 (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)
 

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