23.1.394 problem 379

Internal problem ID [5001]
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 : 379
Date solved : Tuesday, September 30, 2025 at 11:15:46 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.073 (sec). Leaf size: 42

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

\begin{align*} y(x)&\to c_1 \exp \left (\int _1^x\frac {2-2 K[1]^3}{K[1]-2 K[1]^4}dK[1]\right )\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.186 (sec). Leaf size: 17

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

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