74.1.29 problem 36

Internal problem ID [15738]
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 : Monday, March 31, 2025 at 01:46:45 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

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

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

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

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

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

✓ Sympy. Time used: 0.172 (sec). Leaf size: 12

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

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