Internal problem ID [14079]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=\frac {\sqrt {x^{2}-16}}{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x)=sqrt(x^2-16)/x,y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {x^{2}-16}+4 \arctan \left (\frac {4}{\sqrt {x^{2}-16}}\right )+c_{1} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 33
DSolve[y'[x]==Sqrt[x^2-16]/x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -4 \arctan \left (\frac {\sqrt {x^2-16}}{4}\right )+\sqrt {x^2-16}+c_1 \]