63.1.11 problem 11

Internal problem ID [15451]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 11
Date solved : Thursday, October 02, 2025 at 10:14:56 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

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

\[ y = \frac {-x +c_1}{x -1} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 22

ode=(1+y[x])-(1-x)*D[y[x],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: 0.146 (sec). Leaf size: 8

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

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