Internal problem ID [12348]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.3.1, page 57
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=\frac {1}{x^{2}-1}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 10
dsolve([diff(y(x),x)=1/(x^2-1),y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = -\operatorname {arctanh}\left (x \right )+1 \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 23
DSolve[{y'[x]==1/(x^2-1),{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} (\log (1-x)-\log (x+1)+2) \]