12.7.9 problem 9

Internal problem ID [1719]
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 : 9
Date solved : Saturday, March 29, 2025 at 11:36:37 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 6 x y^{2}+2 y+\left (12 x^{2} y+6 x +3\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 24

ode:=6*x*y(x)^2+2*y(x)+(12*x^2*y(x)+6*x+3)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ 3 x^{2} y^{4}+\left (2 x +1\right ) y^{3}+c_1 = 0 \]

✓ Mathematica. Time used: 61.558 (sec). Leaf size: 1544

ode=(6*x*y[x]^2+2*y[x])+(12*x^2*y[x]+6*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)**2 + (12*x**2*y(x) + 6*x + 3)*Derivative(y(x), x) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out