23.1.659 problem 654

Internal problem ID [5266]
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 : 654
Date solved : Tuesday, September 30, 2025 at 12:05:20 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} 2 x \left (5 x^{2}+y^{2}\right ) y^{\prime }&=x^{2} y-y^{3} \end{align*}

✓ Maple. Time used: 0.026 (sec). Leaf size: 29

ode:=2*x*(5*x^2+y(x)^2)*diff(y(x),x) = x^2*y(x)-y(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \operatorname {RootOf}\left (\textit {\_Z}^{5} c_1^{4} x^{4} \sqrt {c_1 x}-\textit {\_Z}^{2}-3\right ) x \]

✓ Mathematica. Time used: 2.585 (sec). Leaf size: 216

ode=2 x(5 x^2+y[x]^2)D[y[x],x]==x^2 y[x]-y[x]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.491 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2*y(x) + 2*x*(5*x**2 + y(x)**2)*Derivative(y(x), x) + y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \log {\left (x \right )} = C_{1} + \log {\left (\frac {\left (3 + \frac {y^{2}{\left (x \right )}}{x^{2}}\right )^{\frac {2}{9}}}{\left (\frac {y{\left (x \right )}}{x}\right )^{\frac {10}{9}}} \right )} \]