74.1.35 problem 42

Internal problem ID [15815]
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 : 42
Date solved : Tuesday, January 28, 2025 at 08:08:04 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 25

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

\[ y = \sqrt {x^{2}-16}+4 \arctan \left (\frac {4}{\sqrt {x^{2}-16}}\right )+c_{1} \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 33

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

\[ y(x)\to -4 \arctan \left (\frac {\sqrt {x^2-16}}{4}\right )+\sqrt {x^2-16}+c_1 \]