23.1.392 problem 377

Internal problem ID [4999]
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 : 377
Date solved : Tuesday, September 30, 2025 at 09:13:46 AM
CAS classification : [_rational, _Riccati]

\begin{align*} x \left (-x^{3}+1\right ) y^{\prime }&=x^{2}+\left (1-2 x y\right ) y \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

ode:=x*(-x^3+1)*diff(y(x),x) = x^2+(1-2*x*y(x))*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x \left (c_1 +x \right )}{c_1 \,x^{2}+1} \]

✓ Mathematica. Time used: 0.427 (sec). Leaf size: 31

ode=x*(1-x^3)*D[y[x],x]==x^2+(1-2*x*y[x])*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.274 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2 + x*(1 - x**3)*Derivative(y(x), x) - (-2*x*y(x) + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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