could u find the equilibria where it is both unstable and stable Find all equilibria, and, by calculating the eigenvalue of the differential equation, determine which equilibria are stable and which are unstable.dydt=y(5-y)(y-6)CWhich equilibria are stable? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.OA. The stable equilibrium/equilibria is/are(Type an integer or a decimal. Use a comma to separate answers as needed.)OB. There are no stable equilibria.

To find the equilibria of the given differential equation and determine their stability, we need to…

Answered: Find all equilibria, and, by…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.8: Applications Of Vector Spaces

Problem 83E

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Find all equilibria for the following system of differential equations and determine the stability of each equilibrium. dx1 = 12x, (1- x1) - 6×,×2 dt dx2 =X2 (6- x2) - 5x2 dt ..... Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The stable equilibria are (X1, X2 and the unstable equilibria are (x1, X2 (Type integers or fractions. Type ordered pairs. Use a comma to separate answers as needed.) O B. The stable equilibria are (x1, x2) =. There are no unstable equilibria. (Type an integer or a fraction. Type an ordered pair. Use a comma to separate answers as needed.) O C. The unstable equilibria are (x1. X2) = |. There are no stable equilibria. (Type an integer or a fraction. Type an ordered pair. Use a comma to separate answers as needed.) D. There are no equilibria.
Classify each differential equation as an ordinary differential equation (ODE) or a partial differential equation (PDE), give the order, and indicate the independent and dependent variables. If the equation is an ODE, indicate whether the equation is linear or nonlinear. d.r - et = 4t – 2 dt ODE or PDE: Order: Independent variable(s): Dependent variable: Linear or nonlinear: du du (b) ODE or PDE: Order: Independent variable(s): Dependent variable: Linear or nonlinear: 1 d³y sin(x)y = x²y I dr3 ODE or PDE: Order: Independent variable(s): Dependent variable: Linear or nonlinear:
Find all equilibria for the following system of differential equations and determine the stability of each equilibrium. dx, 8x1 (1- x4) - 4×,X2 %3D dt dx2 = X2 (5 - X2) - 4x2 dt ...... Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. (1, 2) A. The stable equilibria are (x4, X2 = and the unstable equilibria are (x4, X2 %3D (Type integers or fractions. Type ordered pairs. Use a comma to separate answers as needed.) (*1, X2 В. The unstable equilibria are There are no stable equilibria. (Type an integer or a fraction. Type an ordered pair. Use a comma to separate answers as needed.) С. The stable equilibria are (x,, x,) =. There are no unstable equilibria. (Type an integer or a fraction. Type an ordered pair. Use a comma to separate answers as needed.) O D. There are no equilibria.
Consider the partial differential equation u; + uutz = 3 + uxx. Determine the order of this equation; state whether this equation is linear or nonlinear. Partial derivatives are denoted by subscripts. The equation is The order of the equation is i
For each system of differential equations, sketch the lines in the direction of the eigenvectors . Indicate on each line the direction the solution would move if an initial point is on the line. The equilibrium of both systems is (0,0). Based upon your graph, is the equilibrium stable or unstable. Use your graph to answer the question. dx dt A. dy = dt dt B. dy
A linear second-order non-homogeneous equation models this scenario: People falling at a height of 100ft above the ground attached to a 100-foot rope into a pit that's cut off at 50 feet underground. Spring constant of the rope is 120 lbs/ft, and air resistance is 5 times the instantaneous velocity. Write this scenario as an initial value problem as a system of linear first-order differential equations. Attached is the equation. M is the mass of person falling and g is gravity constant.
Solve the homogeneous differential equation....................,,,,,,,,
Differential Equation. Show the solution.
Look at the differential equation system A. Sketch the zero isoclines of the system B. Determine all the equilibrium solutions of the system. C. Determine which of the equilibria are stable or unstable and explain why. Thank you so much!

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