8.6.12 problem 12

Internal problem ID [782]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 12
Date solved : Saturday, March 29, 2025 at 10:22:28 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 6 x y^{3}+2 y^{4}+\left (9 x^{2} y^{2}+8 x y^{3}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

ode:=6*x*y(x)^3+2*y(x)^4+(9*x^2*y(x)^2+8*x*y(x)^3)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ 3 x^{2} y^{3}+2 x y^{4}+c_1 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 60.152 (sec). Leaf size: 1714

ode=6*x*y[x]^3+2*y[x]^4+(9*x^2*y[x]^2+8*x*y[x]^3)*D[y[x],x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*x*y(x)**3 + (9*x**2*y(x)**2 + 8*x*y(x)**3)*Derivative(y(x), x) + 2*y(x)**4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out