12.6.10 problem 10

Internal problem ID [1689]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number : 10
Date solved : Saturday, March 29, 2025 at 11:31:47 PM
CAS classification : [_rational]

\begin{align*} 2 x^{2}+8 x y+y^{2}+\left (2 x^{2}+\frac {x y^{3}}{3}\right ) y^{\prime }&=0 \end{align*}

✗ Maple

ode:=2*x^2+8*x*y(x)+y(x)^2+(2*x^2+1/3*x*y(x)^3)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(2*x^2+8*x*y[x]+y[x]^2)+(2*x^2+x*y[x]^3/3)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2 + 8*x*y(x) + (2*x**2 + x*y(x)**3/3)*Derivative(y(x), x) + y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out