71.5.8 problem 8

Internal problem ID [14404]
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
Date solved : Tuesday, January 28, 2025 at 06:29:50 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {1}{x^{2}-1} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 10

dsolve([diff(y(x),x)=1/(x^2-1),y(0) = 1],y(x), singsol=all)
 

\[ y = -\operatorname {arctanh}\left (x \right )+1 \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 22

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

\[ y(x)\to \int _0^x\frac {1}{K[1]^2-1}dK[1]+1 \]