82.2.1 problem Ex. 1

Internal problem ID [18648]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 14
Problem number : Ex. 1
Date solved : Thursday, March 13, 2025 at 12:27:17 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 22

ode=(1-x)*D[y[x],x]-(1+y[x])==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.242 (sec). Leaf size: 8

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

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