67.1.17 problem 2.3 (g)

Internal problem ID [16282]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.3 (g)
Date solved : Thursday, October 02, 2025 at 10:45:19 AM
CAS classification : [_quadrature]

\begin{align*} x&=\left (x^{2}-9\right ) y^{\prime } \end{align*}

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

ode:=x = (x^2-9)*diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\ln \left (x^{2}-9\right )}{2}+c_1 \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 18

ode=x==(x^2-9)*D[y[x],x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} \log \left (x^2-9\right )+c_1 \end{align*}

✓ Sympy. Time used: 0.098 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x - (x**2 - 9)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \frac {\log {\left (x^{2} - 9 \right )}}{2} \]