62.12.6 problem Ex 6

Internal problem ID [12781]
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 6
Date solved : Monday, March 31, 2025 at 07:05:09 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: 15

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: 0.135 (sec). Leaf size: 37

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 \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: 0.317 (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)
 

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