Question

Sketch the phase portrait of y” - y’ - 6y = 0, y(0) = 2, y’(0)...

Sketch the phase portrait of y” - y’ - 6y = 0, y(0) = 2, y’(0) = 3 as an autonomous system of two first order equations and discuss the stability and the long time behavior of the solutions.

Homework Answers

Answer #1

Doubt in any step then comment below.. i will explain you.

.

Please thumbs up for this solution.. thanks...

.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Given dy/dx =y(y−3)(1−y)^2 dx (a) Sketch the phase line (portrait) and classify all of the critical...
Given dy/dx =y(y−3)(1−y)^2 dx (a) Sketch the phase line (portrait) and classify all of the critical (equilibrium) points. Use arrows to indicated the flow on the phase line (away or towards a critical point). (b) Next to your phase line, sketch the graph of solutions satisfying the initial conditions: y(0)=0, y(0)=1, y(0)=2, y(0)=3, y(2)=4, y(0)=5.
For the autonomous differential equation dy/dt=1-y^2, sketch a graph of f(y) versus y, identify the equilibrium...
For the autonomous differential equation dy/dt=1-y^2, sketch a graph of f(y) versus y, identify the equilibrium solutions identify them as stable, semistable or unstable, draw the phase line and sketch several graphs of solutions in the ty-plane.
following nonlinear system: x' = 2 sin y, y'= x^2 + 2y − 1 find all...
following nonlinear system: x' = 2 sin y, y'= x^2 + 2y − 1 find all singular points in the domain x, y ∈ [−1, 1],determine their types and stability. Find slopes of saddle separatrices. Use this to sketch the phase portrait in the domain x, y ∈ [−1, 1].
] Consider the autonomous differential equation y 0 = 10 + 3y − y 2 ....
] Consider the autonomous differential equation y 0 = 10 + 3y − y 2 . Sketch a graph of f(y) by hand and use it to draw a phase line. Classify each equilibrium point as either unstable or asymptotically stable. The equilibrium solutions divide the ty plane into regions. Sketch at least one solution trajectory in each region.
Consider the autonomous first-order differential equation dy/dx=4y-(y^3). 1. Classify each critical point as asymptotically stable, unstable,...
Consider the autonomous first-order differential equation dy/dx=4y-(y^3). 1. Classify each critical point as asymptotically stable, unstable, or semi-stable. (DO NOT draw the phase portrait and DO NOT sketch the solution curves) 2. Solve the Bernoulli differential equation dy/dx=4y-(y^3).
a) find all possible solutions of y''+y'-6y=12t b) solve initial value problem of y''+y'-6y=12t, y(0)=1, y'(0)=0
a) find all possible solutions of y''+y'-6y=12t b) solve initial value problem of y''+y'-6y=12t, y(0)=1, y'(0)=0
Solve the following system using augmented matrux methods -3x+6y = 0 -4x +6y = 0 a)...
Solve the following system using augmented matrux methods -3x+6y = 0 -4x +6y = 0 a) The initial matrix is: b) First, perform the Row Operation 1/-3R1->R1. The resulting matrix is: c) Next, perform the operation +3R1+R2->R2. The resulting matrix is: d) Finish simplifying the augmented matrix. The reduced matrix is: e) How many solutions does the system have? f) What are the solutions to the system? x = y =
1) Solve the system of equations. Give your answer as an ordered pair (x,y) {y=−7 {5x-6y=72...
1) Solve the system of equations. Give your answer as an ordered pair (x,y) {y=−7 {5x-6y=72 a) One solution: b) No solution c) Infinite number of solutions 2) Solve the system of equations. Give your answer as an ordered pair (x,y) {x=2 {3x-6y=-30 a) One solution: b) No solution c) Infinite number of solutions
find the general solution. 1- y^6(4)+12y''+36y=0 2-6y^(4)+5y'''+7y''+5y'+y=0 3-y^(4)-4y'''+7y''-6y'+2y=0
find the general solution. 1- y^6(4)+12y''+36y=0 2-6y^(4)+5y'''+7y''+5y'+y=0 3-y^(4)-4y'''+7y''-6y'+2y=0
Differential Equations. Solve the following IVP. Y''(Double Prime) + 6Y'(Prime)+5Y =0, Y'(Prime)(0) =0, Y(0)=1
Differential Equations. Solve the following IVP. Y''(Double Prime) + 6Y'(Prime)+5Y =0, Y'(Prime)(0) =0, Y(0)=1