89.1.1 problem 1

Internal problem ID [24236]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 21
Problem number : 1
Date solved : Thursday, October 02, 2025 at 10:01:09 PM
CAS classification : [_separable]

\begin{align*} \left (1-x \right ) y^{\prime }&=y^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

ode:=(1-x)*diff(y(x),x) = y(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{\ln \left (-1+x \right )+c_1} \]

✓ Mathematica. Time used: 0.15 (sec). Leaf size: 23

ode=(1-x)*D[y[x],{x,1}]==y[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{\log (1-x)-c_1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.156 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((1 - x)*Derivative(y(x), x) - y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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