8.3.9 problem 9

Internal problem ID [685]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 9
Date solved : Monday, January 27, 2025 at 02:57:57 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 15

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

\[ y = -\frac {\left (x +1\right ) c_1}{x -1} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 22

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

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