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

Determine rational exponents, Evaluate following. (a) 625 3/4 Solut...

Evaluate following. (a) 625 3/4 Solution  (a) 625 3/4 Again, let's employ both forms to calculate this one.             625 3/4   =( 625 1/4 ) 3 =(5) 3   = 12

Trigonometric approximation grid, With a compass draw the arc associated wi...

With a compass draw the arc associated with a 720° angle, it looks like a circle. With a protractor, label the angle in multiples of 45° and 30° up to 720°.  Notice 30° and 390° ar

Find Equation of the circle, The line 4x-3y=-12 is tangent at the point (-3...

The line 4x-3y=-12 is tangent at the point (-3,0) and the line 3x+4y=16 is tangent at the point (4,1). find the equation of the circle. solution) well you could first find the ra

1 application of complex analysis in THERMODYNAMICS, Hi, this is EBADULLA ...

Hi, this is EBADULLA its about math assignment. 1 application of complex analysis used in thermodynamics. . what all uses are there in that... plz let mee know this answer.

How many permutations can you make of the word statistics, Q. How many perm...

Q. How many permutations can you make of the word STATISTICS? Solution:  There are 10 letters in the word STATISTICS, i.e. n=10. Three of them are S's, so n 1 =3, three are T'

Solid Mensuration, The two sides of a triangle are 17 cm and 28 cm long, an...

The two sides of a triangle are 17 cm and 28 cm long, and the length of the median drawn to the third side is equal to 19.5 cm. Find the distance from an endpoint of this median to

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