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 : Monday, January 27, 2025 at 03:23:26 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*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 28

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

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

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 26

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

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