Internal problem ID [5380]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {x \left (x^{2}-4\right ) y^{\prime }-1=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 29
dsolve([x*(x^2-4)*diff(y(x),x)=1,y(1) = 0],y(x), singsol=all)
\[ y \relax (x ) = -\frac {\ln \relax (x )}{4}+\frac {\ln \left (x +2\right )}{8}+\frac {\ln \left (x -2\right )}{8}-\frac {\ln \relax (3)}{8}-\frac {i \pi }{8} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 26
DSolve[{x*(x^2-4)*y'[x]==1,{y[1]==0}},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*}