67.7.16 problem 16

Internal problem ID [16461]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 16
Date solved : Thursday, October 02, 2025 at 01:34:08 PM
CAS classification : [_quadrature]

\begin{align*} \left (x^{2}-4\right ) y^{\prime }&=x \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=(x^2-4)*diff(y(x),x) = x; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 18

ode=(x^2-4)*D[y[x],x]==x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} \log \left (x^2-4\right )+c_1 \end{align*}

✓ Sympy. Time used: 0.094 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + (x**2 - 4)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \frac {\log {\left (x^{2} - 4 \right )}}{2} \]