23.1.565 problem 555

Internal problem ID [5172]
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 : 555
Date solved : Tuesday, September 30, 2025 at 11:49:12 AM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 2 x \left (2 x^{2}+y\right ) y^{\prime }+\left (12 x^{2}+y\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 51

ode:=2*x*(2*x^2+y(x))*diff(y(x),x)+(12*x^2+y(x))*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {-2 x^{3}+\sqrt {4 x^{6}+c_1 x}}{x} \\ y &= \frac {-2 x^{3}-\sqrt {4 x^{6}+c_1 x}}{x} \\ \end{align*}

✓ Mathematica. Time used: 0.322 (sec). Leaf size: 58

ode=2*x*(2*x^2+y[x])*D[y[x],x]+(12*x^2+y[x])*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {2 x^3+\sqrt {x \left (4 x^5+c_1\right )}}{x}\\ y(x)&\to \frac {-2 x^3+\sqrt {x \left (4 x^5+c_1\right )}}{x} \end{align*}

✓ Sympy. Time used: 5.949 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*(2*x**2 + y(x))*Derivative(y(x), x) + (12*x**2 + y(x))*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = x^{2} \left (- \sqrt {\frac {C_{1}}{x^{5}} + 4} - 2\right ), \ y{\left (x \right )} = x^{2} \left (\sqrt {\frac {C_{1}}{x^{5}} + 4} - 2\right )\right ] \]