25.1.22 problem 22

Internal problem ID [4234]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 22
Date solved : Monday, January 27, 2025 at 08:43:21 AM
CAS classification : [_separable]

\begin{align*} \left (x^{2}-1\right ) y^{\prime }&=\left (x^{2}+1\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

dsolve((x^2-1)*diff(y(x),x)=(x^2+1)*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {{\mathrm e}^{x} \left (x -1\right ) c_{1}}{x +1} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 25

DSolve[(x^2-1)*D[y[x],x]==(x^2+1)*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {c_1 e^x (x-1)}{x+1} \\ y(x)\to 0 \\ \end{align*}