23.1.593 problem 586

Internal problem ID [5200]
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 : 586
Date solved : Tuesday, September 30, 2025 at 11:54:43 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.134 (sec). Leaf size: 685

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

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

✓ Mathematica. Time used: 55.341 (sec). Leaf size: 331

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

\begin{align*} y(x)&\to \frac {\sqrt [3]{12 c_1 x^6+2 \sqrt {6} \sqrt {c_1 x^6 \left (1+6 c_1 x^6\right )}+1}+\frac {1}{\sqrt [3]{12 c_1 x^6+2 \sqrt {6} \sqrt {c_1 x^6 \left (1+6 c_1 x^6\right )}+1}}+1}{2 x^3}\\ y(x)&\to \frac {2 i \left (\sqrt {3}+i\right ) \sqrt [3]{12 c_1 x^6+2 \sqrt {6} \sqrt {c_1 x^6 \left (1+6 c_1 x^6\right )}+1}-\frac {2 \left (1+i \sqrt {3}\right )}{\sqrt [3]{12 c_1 x^6+2 \sqrt {6} \sqrt {c_1 x^6 \left (1+6 c_1 x^6\right )}+1}}+4}{8 x^3}\\ y(x)&\to \frac {-2 \left (1+i \sqrt {3}\right ) \sqrt [3]{12 c_1 x^6+2 \sqrt {6} \sqrt {c_1 x^6 \left (1+6 c_1 x^6\right )}+1}+\frac {2 i \left (\sqrt {3}+i\right )}{\sqrt [3]{12 c_1 x^6+2 \sqrt {6} \sqrt {c_1 x^6 \left (1+6 c_1 x^6\right )}+1}}+4}{8 x^3}\\ y(x)&\to 0 \end{align*}

✗ Sympy

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

Timed Out