23.1.711 problem 707

Internal problem ID [5318]
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 : 707
Date solved : Tuesday, September 30, 2025 at 12:29:32 PM
CAS classification : [_rational]

\begin{align*} x \left (1-2 x^{2} y^{3}\right ) y^{\prime }+\left (1-2 x^{3} y^{2}\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 809

ode:=x*(1-2*x^2*y(x)^3)*diff(y(x),x)+(1-2*x^3*y(x)^2)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 60.086 (sec). Leaf size: 672

ode=x(1-2 x^2 y[x]^3)D[y[x],x]+(1-2 x^3 y[x]^2)y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {-2 x^3+c_1 x^2+\frac {x^4 (-2 x+c_1){}^2}{\sqrt [3]{-8 x^9+12 c_1 x^8-6 c_1{}^2 x^7+c_1{}^3 x^6-27 x^4+3 \sqrt {3} \sqrt {x^8 \left (16 x^5-24 c_1 x^4+12 c_1{}^2 x^3-2 c_1{}^3 x^2+27\right )}}}+\sqrt [3]{-8 x^9+12 c_1 x^8-6 c_1{}^2 x^7+c_1{}^3 x^6-27 x^4+3 \sqrt {3} \sqrt {x^8 \left (16 x^5-24 c_1 x^4+12 c_1{}^2 x^3-2 c_1{}^3 x^2+27\right )}}}{6 x^2}\\ y(x)&\to \frac {2 x^2 (-2 x+c_1)-\frac {i \left (\sqrt {3}-i\right ) x^4 (-2 x+c_1){}^2}{\sqrt [3]{-8 x^9+12 c_1 x^8-6 c_1{}^2 x^7+c_1{}^3 x^6-27 x^4+3 \sqrt {3} \sqrt {x^8 \left (16 x^5-24 c_1 x^4+12 c_1{}^2 x^3-2 c_1{}^3 x^2+27\right )}}}+i \left (\sqrt {3}+i\right ) \sqrt [3]{-8 x^9+12 c_1 x^8-6 c_1{}^2 x^7+c_1{}^3 x^6-27 x^4+3 \sqrt {3} \sqrt {x^8 \left (16 x^5-24 c_1 x^4+12 c_1{}^2 x^3-2 c_1{}^3 x^2+27\right )}}}{12 x^2}\\ y(x)&\to \frac {2 x^2 (-2 x+c_1)+\frac {i \left (\sqrt {3}+i\right ) x^4 (-2 x+c_1){}^2}{\sqrt [3]{-8 x^9+12 c_1 x^8-6 c_1{}^2 x^7+c_1{}^3 x^6-27 x^4+3 \sqrt {3} \sqrt {x^8 \left (16 x^5-24 c_1 x^4+12 c_1{}^2 x^3-2 c_1{}^3 x^2+27\right )}}}-\left (1+i \sqrt {3}\right ) \sqrt [3]{-8 x^9+12 c_1 x^8-6 c_1{}^2 x^7+c_1{}^3 x^6-27 x^4+3 \sqrt {3} \sqrt {x^8 \left (16 x^5-24 c_1 x^4+12 c_1{}^2 x^3-2 c_1{}^3 x^2+27\right )}}}{12 x^2} \end{align*}

✗ Sympy

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

Timed Out