50.1.29 problem 3(e)

Internal problem ID [7801]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number : 3(e)
Date solved : Wednesday, March 05, 2025 at 05:06:18 AM
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: 0.019 (sec). Leaf size: 28

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

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

✓ Mathematica. Time used: 0.007 (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]
 

\[ y(x)\to \frac {1}{8} \left (\log \left (\frac {1}{3} \left (4-x^2\right )\right )-2 \log (x)\right ) \]

✓ Sympy. Time used: 0.200 (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)
 

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