69.2.11 problem 31

Internal problem ID [17975]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 2. The method of isoclines. Exercises page 27
Problem number : 31
Date solved : Thursday, October 02, 2025 at 02:31:48 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {1+y}{x -1} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

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

\[ y = -1+\left (x -1\right ) c_1 \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 18

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

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

✓ Sympy. Time used: 0.126 (sec). Leaf size: 8

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

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