72.1.37 problem 3 (e)

Internal problem ID [19378]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 3 (e)
Date solved : Thursday, October 02, 2025 at 04:20:00 PM
CAS classification : [_quadrature]

\begin{align*} x \left (x^{2}-4\right ) y^{\prime }&=1 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.045 (sec). Leaf size: 28

ode:=x*(x^2-4)*diff(y(x),x) = 1; 
ic:=[y(1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\ln \left (x -2\right )}{8}-\frac {\ln \left (x \right )}{4}+\frac {\ln \left (x +2\right )}{8}-\frac {i \pi }{8}-\frac {\ln \left (3\right )}{8} \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 26

ode=x*(x^2-4)*D[y[x],x]==1; 
ic={y[1]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{8} \left (\log \left (\frac {1}{3} \left (4-x^2\right )\right )-2 \log (x)\right ) \end{align*}

✓ Sympy. Time used: 0.107 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(x**2 - 4)*Derivative(y(x), x) - 1,0) 
ics = {y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {\log {\left (x \right )}}{4} + \frac {\log {\left (x^{2} - 4 \right )}}{8} - \frac {\log {\left (3 \right )}}{8} - \frac {i \pi }{8} \]