32.6.30 problem Exercise 12.30, page 103

Internal problem ID [5895]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.30, page 103
Date solved : Sunday, March 30, 2025 at 10:24:20 AM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 75

ode:=(6*x*y(x)+x^2+3)*diff(y(x),x)+3*y(x)^2+2*x*y(x)+2*x = 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: 0.644 (sec). Leaf size: 83

ode=(6*x*y[x]+x^2+3)*D[y[x],x]+3*y[x]^2+2*x*y[x]+2*x==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