2.3.9 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 : Tuesday, September 30, 2025 at 04:05:59 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 22

ode=(-x^2+1)*D[y[x],x] == 2*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.154 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((1 - x**2)*Derivative(y(x), x) - 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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