Let (t) =x' (t)==If x (0) ==x₂(t) =21(t)x₂ (t)x₁(t) ==36 x₁(t)-70 x₁(t)-1A-4Put the eigenvalues in ascending order when you enter x₁(t), ₂(t) below.be a solution to the system of differential equations:+ 21x₂ (t)41 *₂ (t)find ä(t).exp(t)+ exp( |exp(t)+exp(|t)t)

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Answered: Let r(t) = x' (t) x₂ (t) 21(t) [-]…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Solve the system of first-order linear differential equations. (Use C1 and C2 as constants.) Yı' = 3y1 y2' = Y2 (y1(t), y2(t))
Suppose tx1 + 2x2 + sec(t), sin(t)x1+ tx2 – 3. This system of linear differential equations can be put in the form æ' = P(t)æ + g(t). Determine P(t) and g(t). P(t) = g(t) =
1. Find real-valued fundamental solutions of the differential equation x' = Ax, where matrix A has eigenvalues and eigenvectors - [₁4] - 6.2) A₁ = −2+i V₁ = A2 = -2-i V2 =
2. Consider the eigenvalue problem, y" + Ay = 0, for 0 < x < 7/2; y' (0) = 0, y(n/2) = 0. Find all eigenvalues and eigenfunctions for the case where the auxiliary equation has complex roots.
Consider a system of differential equations describing the progress of a disease in a population, given by In our particular case, this is: a) Find the nullclines (simplest form) of this system of differential equations. The x-nullcline is y = x = 3-3xy - 1x y = 3xy - 2y where x (t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of individuals is counted in units of 1,000 individuals. The y-nullclines are y = and x = b) There are two equilibrium points that are biologically meaningful (i.e. whose coordinates are non-negative). They are (x1,9₁) and (x2, y2), where we order them so that x1 < x2. The equilibrium with the smaller x-coordinate is (x₁, y₁) : The equilibrium with the larger x-coordinate is (x2, y₂) = where A = 0 sin (a) c) The linearization of the system of differential equations at the equilibrium (ï1, Y₁) gives a system of the form (+) ¹ (~), f əx ∞ a Ω = A x' G E = F(x, y) for a vector-valued function…
Transfer the following differential equation: - 4t y" + 3y" + 2y' — 5y = t² + e²¯ into a system of first order differential equations in the form of x' Ax + ģ(t) What are , A, and ģ(t)? = x(t) x (t) x (t) x (t) = = = = x₁ (t) x₂ (t) x3 (t). x₁ (t) x₂ (t) x3 (t). [T₁ (t)] x₂ (t) x3 (t). X1 x₁ (t) = = = Y Y D C Y x₂ (t) - = x3 (t). Y y' 2 " A = A - A = cos t A = 0 5 1 0 5 1 0 0 1 -2 -3 0 1 0 EH -5 2 3 0 0 1 1 0 1 -2 -3 -3 1 0 0 1 -2 5 " 0 0 1 g(t) 2 2 g(t) " g(t) = g(t) = = e -4t 0 0 +e-4t cos(t). + e t² 0 0 -4t cos(t) cos(t). 0 0 t² + e-4t cos(t).
Transform the given system of differential equations into an equivalent system of first-order differential equations. x' - 3x' - 5x+2y=0 y'' +6y' - 6x-3y = sin t Let x₁ = x, X₂ = X', Y₁ = y, and y₂ = y'. Complete the system below. X₁' X₂ X Y2 II 11 11 11
1. Find a system of first-order differential equations that correspond to the given second order differential equation: t²u" + 3tu' +u = t² + 2 Show all steps, including which new variables you are assigning to which terms.

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