Find and classify all the equilibrium solutions, Mathematics

Assignment Help:

Find and classify all the equilibrium solutions to the subsequent differential equation.

y' = y2 - y - 6

Solution

First, get the equilibrium solutions. It is generally easy adequate to do.

y2 - y - 6 = (y - 3) ( y + 2) = 0

Thus, it looks as we've found two equilibrium solutions. y = -2 and y = 3 both are equilibrium solutions. There is the sketch of several integral curves for this differential equation is given below. A sketch of the integral curves or direction fields can simplify the method of classifying the equilibrium solutions.

1887_Find and classify all the equilibrium solutions.png

By this sketch it appears that solutions which start "near" y = -2 all move indirections of it as t rises and so y = -2 is an asymptotically stable equilibrium solution and solutions which start "near" y = 3 all move away from it as t raises and so y = 3 is an unstable equilibrium solution.

This next illustration will introduce the third classification which we can give to equilibrium solutions.


Related Discussions:- Find and classify all the equilibrium solutions

How many ways can dvds be arranged on a shelf, How many ways can 4 DVDs be ...

How many ways can 4 DVDs be arranged on a shelf? Solution: There are 4 ways to choose the first DVD, 3 ways to choose the second, 2 ways to choose the third and 1 way to choo

What is the marginal product of labor function, Your engineering department...

Your engineering department estimated the following production function. Q = 15L 2 - 0.5L 3 a. What is the marginal product of labor function, MP L ? b. What is the aver

Find the height of the building, A building is in the form of a cylinder su...

A building is in the form of a cylinder surrounded by a hemispherical vaulted dome and contains   41(19/21-) cu m of air. If the internal diameter of the building is equal to its t

Linear programming problem, I have a linear programming problem that we are...

I have a linear programming problem that we are to work out in QM for Windows and I can''t figure out how to lay it out. Are you able to help me if I send you the problem?

Give an equations with the variable on both sides, Give an Equations with t...

Give an Equations with the variable on both sides ? Many equations that you encounter will have variables on both sides. Some of these equations will even contain grouping sy

Divison, what is 24 diveded by 3

what is 24 diveded by 3

Maths Assessment, Assessment task This Term Assessment will require you ass...

Assessment task This Term Assessment will require you assess the effectiveness of your current lunch budget and prepare a proposal to your caregiver to seek permission to be given

Geometry, which kind of triangle has no congruent sides ?

which kind of triangle has no congruent sides ?

Probability, An unbiased die is tossed twice .Find the probability of getti...

An unbiased die is tossed twice .Find the probability of getting a 4,5,6 on the first toss and a 1,2,3,4 on the second toss

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd