Internal problem ID [11649]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 5, Trivial differential equations. Exercises page 33
Problem number: 5.1 (ii).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=\frac {1}{x^{2}-1}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 10
dsolve(diff(y(x),x)=1/(x^2-1),y(x), singsol=all)
\[ y \left (x \right ) = -\operatorname {arctanh}\left (x \right )+c_{1} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 26
DSolve[y'[x]==1/(x^2-1),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} (\log (1-x)-\log (x+1)+2 c_1) \]