68.1.35 problem 42

Internal problem ID [17102]
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 : Thursday, October 02, 2025 at 01:43:13 PM
CAS classification : [_quadrature]

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

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

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

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

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to -4 \arctan \left (\frac {\sqrt {x^2-16}}{4}\right )+\sqrt {x^2-16}+c_1 \end{align*}

✓ Sympy. Time used: 0.468 (sec). Leaf size: 80

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

\[ y{\left (x \right )} = C_{1} + \begin {cases} - \frac {i x}{\sqrt {-1 + \frac {16}{x^{2}}}} - 4 i \operatorname {acosh}{\left (\frac {4}{x} \right )} + \frac {16 i}{x \sqrt {-1 + \frac {16}{x^{2}}}} & \text {for}\: \frac {1}{\left |{x^{2}}\right |} > \frac {1}{16} \\\frac {x}{\sqrt {1 - \frac {16}{x^{2}}}} + 4 \operatorname {asin}{\left (\frac {4}{x} \right )} - \frac {16}{x \sqrt {1 - \frac {16}{x^{2}}}} & \text {otherwise} \end {cases} \]