62.12.19 problem Ex 20

Internal problem ID [12794]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 19. Summary. Page 29
Problem number : Ex 20
Date solved : Monday, March 31, 2025 at 07:07:56 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 2.095 (sec). Leaf size: 21

ode=(1-x)*y[x]-(1+y[x])*x*D[y[x],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: 0.263 (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)
 

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