23.1.569 problem 559

Internal problem ID [5176]
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 : 559
Date solved : Tuesday, September 30, 2025 at 11:50:01 AM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (3+6 x y+x^{2}\right ) y^{\prime }+2 x +2 x y+3 y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 75

ode:=(3+6*x*y(x)+x^2)*diff(y(x),x)+2*x+2*x*y(x)+3*y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {-x^{2}-3+\sqrt {x^{4}-12 x^{3}-12 c_1 x +6 x^{2}+9}}{6 x} \\ y &= \frac {-x^{2}-3-\sqrt {x^{4}-12 x^{3}-12 c_1 x +6 x^{2}+9}}{6 x} \\ \end{align*}

✓ Mathematica. Time used: 0.413 (sec). Leaf size: 83

ode=(3+6*x*y[x]+x^2)*D[y[x],x]+2*x+2*x*y[x]+3*y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {x^2+\sqrt {x^4-12 x^3+6 x^2+36 c_1 x+9}+3}{6 x}\\ y(x)&\to -\frac {x^2-\sqrt {x^4-12 x^3+6 x^2+36 c_1 x+9}+3}{6 x} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*y(x) + 2*x + (x**2 + 6*x*y(x) + 3)*Derivative(y(x), x) + 3*y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out