23.1.668 problem 663

Internal problem ID [5275]
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 : 663
Date solved : Tuesday, September 30, 2025 at 12:06:28 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} x \left (x^{2}-6 y^{2}\right ) y^{\prime }&=4 \left (x^{2}+3 y^{2}\right ) y \end{align*}

✓ Maple. Time used: 0.272 (sec). Leaf size: 53

ode:=x*(x^2-6*y(x)^2)*diff(y(x),x) = 4*(x^2+3*y(x)^2)*y(x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {c_1 \left (-1+\sqrt {\frac {-24 x^{6}+c_1^{2}}{c_1^{2}}}\right )}{12 x^{2}} \\ y &= \frac {c_1 \left (1+\sqrt {\frac {-24 x^{6}+c_1^{2}}{c_1^{2}}}\right )}{12 x^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.588 (sec). Leaf size: 67

ode=x(x^2-6 y[x]^2)D[y[x],x]==4(x^2+3 y[x]^2)y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^{c_1}-\sqrt {-24 x^6+e^{2 c_1}}}{12 x^2}\\ y(x)&\to \frac {\sqrt {-24 x^6+e^{2 c_1}}+e^{c_1}}{12 x^2} \end{align*}

✓ Sympy. Time used: 1.728 (sec). Leaf size: 51

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(x**2 - 6*y(x)**2)*Derivative(y(x), x) - (4*x**2 + 12*y(x)**2)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {- \sqrt {- 24 x^{6} + e^{6 C_{1}}} + e^{3 C_{1}}}{12 x^{2}}, \ y{\left (x \right )} = \frac {\sqrt {- 24 x^{6} + e^{6 C_{1}}} + e^{3 C_{1}}}{12 x^{2}}\right ] \]