Internal problem ID [5379]
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(d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (x^{2}-1\right ) y^{\prime }-1=0} \end {gather*} With initial conditions \begin {align*} [y \relax (2) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 15
dsolve([(x^2-1)*diff(y(x),x)=1,y(2) = 0],y(x), singsol=all)
\[ y \relax (x ) = -\arctanh \relax (x )+\arctanh \left (\frac {1}{2}\right )-\frac {i \pi }{2} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 27
DSolve[{(x^2-1)*y'[x]==1,{y[2]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} (\log (3-3 x)-\log (x+1)-i \pi ) \\ \end{align*}