23.1.723 problem 719

Internal problem ID [5330]
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 : 719
Date solved : Tuesday, September 30, 2025 at 12:30:28 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 0.024 (sec). Leaf size: 37

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

\[ \ln \left (x \right )-c_1 -\frac {5 \ln \left (\frac {y}{x^{{3}/{5}}}\right )}{2}+\frac {5 \ln \left (\frac {4 y^{5}-x^{3}}{x^{3}}\right )}{8} = 0 \]

✓ Mathematica. Time used: 1.525 (sec). Leaf size: 141

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

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

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (x**3 - y(x)**5)*y(x)/(x*(x**3 + y(x)**5))