23.1.546 problem 536

Internal problem ID [5153]
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 : 536
Date solved : Tuesday, September 30, 2025 at 11:46:06 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x \left (4 x -y\right ) y^{\prime }+4 x^{2}-6 x y-y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.076 (sec). Leaf size: 69

ode:=x*(4*x-y(x))*diff(y(x),x)+4*x^2-6*x*y(x)-y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {-4 x^{2} c_1^{2}+\sqrt {-12 x^{2} c_1^{2}+1}+1}{2 c_1^{2} x} \\ y &= \frac {-4 x^{2} c_1^{2}-\sqrt {-12 x^{2} c_1^{2}+1}+1}{2 c_1^{2} x} \\ \end{align*}

✓ Mathematica. Time used: 0.804 (sec). Leaf size: 90

ode=x*(4*x -y[x])*D[y[x],x]+4*x^2-6*x*y[x]-y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {4 x^2+e^{\frac {c_1}{2}} \sqrt {12 x^2+e^{c_1}}+e^{c_1}}{2 x}\\ y(x)&\to -\frac {4 x^2-e^{\frac {c_1}{2}} \sqrt {12 x^2+e^{c_1}}+e^{c_1}}{2 x} \end{align*}

✓ Sympy. Time used: 1.751 (sec). Leaf size: 53

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

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