81.2.6 problem 3-7

Internal problem ID [21495]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 3. Exact differential equations. Page 42.
Problem number : 3-7
Date solved : Thursday, October 02, 2025 at 07:42:06 PM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 51

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

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

✓ Mathematica. Time used: 0.094 (sec). Leaf size: 65

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

\begin{align*} y(x)&\to \frac {1}{2} \left (-x^3-\sqrt {x^6+12 x^2+4 c_1}\right )\\ y(x)&\to \frac {1}{2} \left (-x^3+\sqrt {x^6+12 x^2+4 c_1}\right ) \end{align*}

✗ Sympy

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

Timed Out