23.1.391 problem 376

Internal problem ID [4998]
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 : 376
Date solved : Tuesday, September 30, 2025 at 09:13:44 AM
CAS classification : [_linear]

\begin{align*} x \left (-x^{3}+1\right ) y^{\prime }&=2 x -\left (-4 x^{3}+1\right ) y \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=x*(-x^3+1)*diff(y(x),x) = 2*x-(-4*x^3+1)*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-x^{2}+c_1}{x^{4}-x} \]

✓ Mathematica. Time used: 10.07 (sec). Leaf size: 89

ode=x*(1-x^3)*D[y[x],x]==2*x-(1-4*x^3)*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \exp \left (\int _1^x-\frac {1-4 K[1]^3}{K[1]-K[1]^4}dK[1]\right ) \left (\int _1^x-\frac {2 \exp \left (-\int _1^{K[2]}-\frac {1-4 K[1]^3}{K[1]-K[1]^4}dK[1]\right )}{K[2]^3-1}dK[2]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.184 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(1 - x**3)*Derivative(y(x), x) - 2*x + (1 - 4*x**3)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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