81.2.10 problem 3-11

Internal problem ID [21499]
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 : 3-11
Date solved : Thursday, October 02, 2025 at 07:42:11 PM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

\begin{align*} 3 x^{2}+4 y x +\left (2 x^{2}+2 y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 49

ode:=3*x^2+4*x*y(x)+(2*x^2+2*y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.091 (sec). Leaf size: 53

ode=(3*x^2+4*x*y[x])+(2*x^2+2*y[x])*D[y[x],x] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x**2 + 4*x*y(x) + (2*x**2 + 2*y(x))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out