44.5.24 problem 24

Internal problem ID [7086]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 24
Date solved : Sunday, March 30, 2025 at 11:40:08 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {y^{2}-1}{x^{2}-1} \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=2 \end{align*}

✓ Maple. Time used: 0.057 (sec). Leaf size: 5

ode:=diff(y(x),x) = (-1+y(x)^2)/(x^2-1); 
ic:=y(2) = 2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = x \]

✓ Mathematica. Time used: 4.048 (sec). Leaf size: 6

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

\[ y(x)\to x \]

✓ Sympy. Time used: 0.486 (sec). Leaf size: 3

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

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