68.1.37 problem 44

Internal problem ID [17104]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 44
Date solved : Thursday, October 02, 2025 at 01:43:14 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {1}{x^{2}-16} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=diff(y(x),x) = 1/(x^2-16); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\ln \left (x -4\right )}{8}-\frac {\ln \left (x +4\right )}{8}+c_1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 23

ode=D[y[x],x]==1/(x^2-16); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _1^x\frac {1}{K[1]^2-16}dK[1]+c_1 \end{align*}

✓ Sympy. Time used: 0.092 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - 1/(x**2 - 16),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \frac {\log {\left (x - 4 \right )}}{8} - \frac {\log {\left (x + 4 \right )}}{8} \]