86.1.10 problem 10

Internal problem ID [23072]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 3. Some standard types of differential equations. Exercise 3b at page 43
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:18:51 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to 1+c_1 \sqrt {x^2-1}\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.247 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = C_{1} \sqrt [4]{2 x - 1} e^{\frac {x}{2}} + 1 \]