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

Draw a common graph f ( x ) = |x|, Graph f ( x ) = |x| Solution The...

Graph f ( x ) = |x| Solution There actually isn't much to in this problem outside of reminding ourselves of what absolute value is. Remember again that the absolute value f

Geometyr, Lines EF and GH are graphed on this coordinate plane. Which point...

Lines EF and GH are graphed on this coordinate plane. Which point is the intersection of lines EF and GH?

Prove that ar= 3/7 ac of parallelogram , ABCD is a parallelogram in the giv...

ABCD is a parallelogram in the given figure, AB is divided at P and CD and Q so that AP:PB=3:2 and CQ:QD=4:1. If PQ meets AC at R, prove that AR= 3/7 AC. Ans:    ΔAPR ∼ Δ

Convergence, Assume that (xn) is a sequence of real numbers and that a, b €...

Assume that (xn) is a sequence of real numbers and that a, b € R with a is not eaqual to 0. (a) If (x n ) converges to x, show that (|ax n + b|) converges to |ax + b|. (b) Give

Binomial, how do you find the co=efficent when there are two brackets invol...

how do you find the co=efficent when there are two brackets involved?

What are inclusive events, Q. What are Inclusive Events? Ans. Even...

Q. What are Inclusive Events? Ans. Events that can occur at the same time are called inclusive events. For example, a student can belong to more than one club at one time

Multiple, what number does not belong 43,47,53,59,65,67

what number does not belong 43,47,53,59,65,67

Derivatives to physical systems, Derivatives to Physical Systems: A st...

Derivatives to Physical Systems: A stone is dropped into a quiet lake, & waves move within circles outward from the location of the splash at a constant velocity of 0.5 feet p

Geometry, RS=8y+4 ST=4y+8 RT=15y-9 a.) WHAT IS THE VALUE OF y b.) FIND RS...

RS=8y+4 ST=4y+8 RT=15y-9 a.) WHAT IS THE VALUE OF y b.) FIND RS, ST, AND RT

Infinite, why cant we find the value of 1 upon zero

why cant we find the value of 1 upon zero

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