23.1.376 problem 361

Internal problem ID [4983]
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 : 361
Date solved : Tuesday, September 30, 2025 at 09:08:47 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

\[ y = \frac {c_1 x}{\left (x +1\right )^{{3}/{2}} \sqrt {x -1}} \]

✓ Mathematica. Time used: 0.056 (sec). Leaf size: 44

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

\begin{align*} y(x)&\to c_1 \exp \left (\int _1^x\frac {K[1]^2-K[1]+1}{K[1]-K[1]^3}dK[1]\right )\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.215 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = \frac {C_{1} x}{\sqrt {x - 1} \left (x + 1\right )^{\frac {3}{2}}} \]