12.7.11 problem 11

Internal problem ID [1721]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page 91
Problem number : 11
Date solved : Saturday, March 29, 2025 at 11:36:42 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 12 x^{3} y+24 x^{2} y^{2}+\left (9 x^{4}+32 x^{3} y+4 y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=12*x^3*y(x)+24*x^2*y(x)^2+(9*x^4+32*x^3*y(x)+4*y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ 3 x^{4} y^{3}+8 x^{3} y^{4}+y^{4}+c_1 = 0 \]

✓ Mathematica. Time used: 61.712 (sec). Leaf size: 1733

ode=(12*x^3*y[x]+24*x^2*y[x]^2)+(9*x^4+32*x^3*y[x]+4*y[x])*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(12*x**3*y(x) + 24*x**2*y(x)**2 + (9*x**4 + 32*x**3*y(x) + 4*y(x))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out