74.1.29 problem 36

Internal problem ID [15809]
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 : 36
Date solved : Tuesday, January 28, 2025 at 08:08:00 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 17

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

\[ y(x)\to \sqrt {x^2-16}+c_1 \]