The system of first order differential equationsy₁ = -6y₁ + 8y2 + 1y₂ = 8y16y2 + 1where y₁ (0) = 0, y₂ (0) = 0has solutiony₁ (t)=Y2y₂(t) =

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Answered: The system of first order differential…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Solve the system of differential equations.{x1'=6x1−2x2x2'=2x1+10x2{x1′=6x1-2x2x2′=2x1+10x2x1(0)=16, x2(0)=−16x1(0)=16, x2(0)=-16x1(t)x1(t) = x2(t)x2(t) =
The differential equation 3xy² - 10xy + (3x²y — 5x² - 2) Has solutions of form F(x, y) dy dx = c where = F(x, y) = 0
You solve a second order linear differential equation with constant coefficients and find its complimentary function yo(x) = Ae²+ Be-2 and its particular solution y₂(x) = -x- Apply the conditions (0) = 0 and y/ (0) = 1 to determine the values of A and B. What is the general solution?
The system of first order differential equations has solution y₁ (t) = y₂ (t) = Sy/₁ 13/12 = -7 y₁ - 4 y2, 8 y₁ + 5y2, y₁ (0) Y₂ (0) = -1 = 8
3. Find all equilibrium values of the system of differential equations: dx dt (a) (b) { (c) 14x2x² - xy = = 16y - 2y² - xy = dt x' = x(x − y + 1) y' = y(y + 2x) dx dt dy dt = = x - x² - 2xy 2y - 2y² - 3xy
where A system of system of first-order linear differential equations has the form y' = Ay y' = , y = Y1 Y2 , A = a11 a21 This gives us the system B [an an2 ann] Solve the system of linear differential equations by following the steps listed. y₁ = y₁ 432 y₂ = -2y1 + 8y2 a12 022 ain a2n ⠀ (a) We first want to write this as a matrix equation y'= Ay. List out what the matrix A should be in this matrix equation. (b) We would like to have the equations so that y is a function of only y₁ and ₂2 is a function of only y2. To do this, we want to turn A into a diagonal matrix. This can be done by taking the diagonalization of A. Diagonalize the matrix A you created in part a. (c) Now that we have a matrix P such that P-¹AP = D is diagonal, we substitute y' and y to be Pw' = y Pw=y Pw = APw Since P is invertible, we can multiply P-1 to the left on both sides of the equations to get w = P-¹APW = Dw Write out what the system of linear differential equations looks like now. (d) Let k be any scalar.…

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The system of first order differential equations y₁ = -6y₁ + 8y2 + 1 y₂ = 8y1 - 6y2 + 1 where y₁ (0) = 0, y₂ (0) = 0 has solution y₁ (t)= 2 (t) =