38.1.10 problem 11

Internal problem ID [8171]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 11
Date solved : Tuesday, September 30, 2025 at 05:18:04 PM
CAS classification : [_separable]

\begin{align*} y^{2}-1+x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 9

ode:=y(x)^2-1+x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \tanh \left (\ln \left (x \right )+c_1 \right ) \]

✓ Mathematica. Time used: 0.309 (sec). Leaf size: 40

ode=(y[x]^2-1)+x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.187 (sec). Leaf size: 12

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

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