78.1.37 problem 3 (e)

Internal problem ID [18092]
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 : Tuesday, January 28, 2025 at 11:26:01 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*}

✓ Solution by Maple

Time used: 0.039 (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: 0.006 (sec). Leaf size: 26

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

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