34.2.1 problem 1

Internal problem ID [6031]
Book : A treatise on ordinary and partial differential equations by William Woolsey Johnson. 1913
Section : Chapter 2, Equations of the first order and degree. page 20
Problem number : 1
Date solved : Wednesday, March 05, 2025 at 12:10:02 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 4.161 (sec). Leaf size: 28

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

✓ Sympy. Time used: 0.313 (sec). Leaf size: 12

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

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