23.1.722 problem 718

Internal problem ID [5329]
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 : 718
Date solved : Tuesday, September 30, 2025 at 12:30:25 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} \left (x^{2}-y^{5}\right ) y^{\prime }&=2 x y \end{align*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 25

ode:=(x^2-y(x)^5)*diff(y(x),x) = 2*x*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \operatorname {RootOf}\left (x^{8} \textit {\_Z}^{5}+4-{\mathrm e}^{\frac {8 c_1}{5}} \textit {\_Z} \right ) x^{2} \]

✓ Mathematica. Time used: 1.381 (sec). Leaf size: 121

ode=(x^2-y[x]^5)D[y[x],x]==2 x y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \text {Root}\left [\text {$\#$1}^5+4 \text {$\#$1} c_1+4 x^2\&,1\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^5+4 \text {$\#$1} c_1+4 x^2\&,2\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^5+4 \text {$\#$1} c_1+4 x^2\&,3\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^5+4 \text {$\#$1} c_1+4 x^2\&,4\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^5+4 \text {$\#$1} c_1+4 x^2\&,5\right ]\\ y(x)&\to 0 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x*y(x) + (x**2 - y(x)**5)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -2*x*y(x)/(x**2 - y(x)**5) + Derivative(y(x), x) cannot be solve