74.1.37 problem 44

Internal problem ID [15817]
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 : Tuesday, January 28, 2025 at 08:08:06 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 23

DSolve[D[y[x],x]==1/(x^2-16),y[x],x,IncludeSingularSolutions -> True]
 

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