23.1.724 problem 720

Internal problem ID [5331]
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 : 720
Date solved : Tuesday, September 30, 2025 at 12:30:30 PM
CAS classification : [_rational]

\begin{align*} x^{3} \left (1+5 x^{3} y^{7}\right ) y^{\prime }+\left (3 x^{5} y^{5}-1\right ) y^{3}&=0 \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 25

ode:=x^3*(1+5*x^3*y(x)^7)*diff(y(x),x)+(3*x^5*y(x)^5-1)*y(x)^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ -y^{5} x^{3}-\frac {1}{2 x^{2}}+\frac {1}{2 y^{2}}+c_1 = 0 \]

✓ Mathematica. Time used: 4.964 (sec). Leaf size: 253

ode=x^3(1+5 x^3 y[x]^7)D[y[x],x]+(3 x^5 y[x]^5-1)y[x]^3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \text {Root}\left [2 \text {$\#$1}^7 x^5+\text {$\#$1}^2 \left (1-2 c_1 x^2\right )-x^2\&,1\right ]\\ y(x)&\to \text {Root}\left [2 \text {$\#$1}^7 x^5+\text {$\#$1}^2 \left (1-2 c_1 x^2\right )-x^2\&,2\right ]\\ y(x)&\to \text {Root}\left [2 \text {$\#$1}^7 x^5+\text {$\#$1}^2 \left (1-2 c_1 x^2\right )-x^2\&,3\right ]\\ y(x)&\to \text {Root}\left [2 \text {$\#$1}^7 x^5+\text {$\#$1}^2 \left (1-2 c_1 x^2\right )-x^2\&,4\right ]\\ y(x)&\to \text {Root}\left [2 \text {$\#$1}^7 x^5+\text {$\#$1}^2 \left (1-2 c_1 x^2\right )-x^2\&,5\right ]\\ y(x)&\to \text {Root}\left [2 \text {$\#$1}^7 x^5+\text {$\#$1}^2 \left (1-2 c_1 x^2\right )-x^2\&,6\right ]\\ y(x)&\to \text {Root}\left [2 \text {$\#$1}^7 x^5+\text {$\#$1}^2 \left (1-2 c_1 x^2\right )-x^2\&,7\right ] \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*(5*x**3*y(x)**7 + 1)*Derivative(y(x), x) + (3*x**5*y(x)**5 - 1)*y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out