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

Objectives of learning to count, Objectives :  After studying this unit, y...

Objectives :  After studying this unit, you should be able to : 1.   explain the processes involved in counting; 2.   explain why the ability to recite number names is no in

complex number z, For complex number z, the minimum value of |z| + |z - co...

For complex number z, the minimum value of |z| + |z - cosa - i sina|+|z - 2(cosa + i sina )| is..? Solution) |z| + |z-(e^ia)| + |z-2(e^ia)| we see.....oigin , e^ia , 2e^ia ,  f

Understand the terms quotient and remainder, What other activities can you ...

What other activities can you suggest to help a child understand the terms 'quotient' and 'remainder'? Once children understand the concept and process of division, with enough

Evaluate limit, Evaluate the given limit. Solution: In this quest...

Evaluate the given limit. Solution: In this question none of the earlier examples can help us. There's no factoring or simplifying to accomplish.  We can't rationalize &

Prove sum of squares any two sides equal twice square, Prove that in any tr...

Prove that in any triangle the sum of the squares of any two sides is equal to twice the square of half of the third side together with twice the square of the median, which bisect

Compound interest, you have RM5O,OOO to invest,and two fund that you''d li...

you have RM5O,OOO to invest,and two fund that you''d like to invest in.The You-Risk-It Fund yields 14% interest.The Extra-Dull Fund yields 6% interest.Besause of college financial-

Complex numbers from the eigenvector and the eigenvalue, Complex numbers fr...

Complex numbers from the eigenvector and the eigenvalue. Example1 : Solve the following IVP. We first require the eigenvalues and eigenvectors for the given matrix.

How far is balloon from the shore, Steve Fossett is going the shores of Aus...

Steve Fossett is going the shores of Australia on the ?rst successful solo hot air balloon ride around the world. His balloon, the Bud Light Spirit of Freedom, is being escorted

Trigonometry, TRIGONOMETRY : "The  mathematician  is  fascinated  with  the...

TRIGONOMETRY : "The  mathematician  is  fascinated  with  the  marvelous  beauty  of the forms  he  constructs,  and  in their  beauty  he  finds  everlasting  truth." Example:

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