Find and classify the differential equation, Mathematics

Assignment Help:

Find and classify the equilibrium solutions of the subsequent differential equation.

y' = y2 - y - 6

Solution

The equilibrium solutions are to such differential equation are y = -2, y = 2, and y = -1. There is the sketch of the integral curves as:

243_Find and classify the differential equation.png

From above it is clear ash hopefully that y = 2 is an unstable equilibrium solution as well as y = -2 is an asymptotically stable equilibrium solution. Though, y = -1 behaves differently from either of these two. Solutions which start above it move indirections of y = -1 whereas solutions that begin below y = -1 move away as t raises.

In cases where solutions on individual side of an equilibrium solution move in the directions of the equilibrium solution and on the other side of the equilibrium solution back off from it we say this as the equilibrium solution semi-stable.

Thus, y = -1 is a semi-stable equilibrium solution.


Related Discussions:- Find and classify the differential equation

Addition, #questiowhat is 1+1n..

#questiowhat is 1+1n..

What is the value of m+n, Every point (x,y) on the curve y=log2 3x is trans...

Every point (x,y) on the curve y=log2 3x is transferred to a new point by the following translation (x',y')=(x+m,y+n), where m and n are integers. The set of (x',y') form the curve

Rejection and acceptance regions, Rejection and Acceptance regions All ...

Rejection and Acceptance regions All possible values which a test statistic may either suppose consistency along with the null hypothesis as acceptance region or lead to the re

#title.automotive cruise control system., What are some of the interestingm...

What are some of the interestingmodern developments in cruise control systems that contrast with comparatively basic old systems

Radius of convergence - sequences and series, Radius of Convergence We ...

Radius of Convergence We will be capable to illustrate that there is a number R so that the power series will converge for, |x - a| R.  This number is known as the radius of

Calculus, what is a domain of a function?

what is a domain of a function?

Unit vector and zero vectors, Unit Vector and Zero Vectors Unit Vec...

Unit Vector and Zero Vectors Unit Vector Any vector along with magnitude of 1, that is || u → || = 1, is called a unit vector. Zero Vectors The vector w → = (

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