23.1.301 problem 291

Internal problem ID [4908]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 291
Date solved : Tuesday, September 30, 2025 at 08:56:18 AM
CAS classification : [_separable]

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+2 x y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=(-x^2+1)*diff(y(x),x)+2*x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,x^{2}-c_1 \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 18

ode=(1-x^2)*D[y[x],x]+2*x*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 \left (x^2-1\right )\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.135 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = C_{1} \left (x^{2} - 1\right ) \]