7.3.9 problem 9

Internal problem ID [49]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 9
Date solved : Saturday, March 29, 2025 at 04:27:44 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (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: 0.028 (sec). Leaf size: 22

ode=(1-x^2)*D[y[x],x]==2*y[x]; 
DSolve[ode,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: 0.259 (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)
 

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