23.1.296 problem 286

Internal problem ID [4903]
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 : 286
Date solved : Tuesday, September 30, 2025 at 08:56:07 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

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

\[ y = \sqrt {x -1}\, \sqrt {x +1}\, c_1 +1 \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to 1+c_1 \sqrt {x^2-1}\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.166 (sec). Leaf size: 14

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

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