73.1.18 problem 2.3 (h)

Internal problem ID [14925]
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 (h)
Date solved : Monday, March 31, 2025 at 01:04:07 PM
CAS classification : [_quadrature]

\begin{align*} 1&=\left (x^{2}-9\right ) y^{\prime } \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

ode:=1 = (x^2-9)*diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\ln \left (x -3\right )}{6}-\frac {\ln \left (x +3\right )}{6}+c_1 \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 23

ode=1==(x^2-9)*D[y[x],x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \int _1^x\frac {1}{K[1]^2-9}dK[1]+c_1 \]

✓ Sympy. Time used: 0.196 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(x**2 - 9)*Derivative(y(x), x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \frac {\log {\left (x - 3 \right )}}{6} - \frac {\log {\left (x + 3 \right )}}{6} \]