AFind the solution of the initial value problemsÿ i= -Y,t Sy zy. (0) = 0%3D: - Y, + Yzy z(0) =42the associatedmatrix of the system is :whereブフ

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Answered: (A Find the solution of the initial…

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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1. for the case of repeated real roots what would the general solution be?2. if i was to let y1(t) = theta(t) as well as y2(t) = theta'(t)=y1'(t) how could i show that the initial equation could be written as a system of 1st order odes that involved y1 and y2. the system will then need to be presented as a the matrix equation y' = My
Consider the initial value problem 0 - 1 x+ 2t ㅇ *(0): Form the complementary solution to the homogeneous equation. x.(t) = a1 + a2 help (formulas) help atrices) Construct a particular solution by assuming the form x,(t) = äe21 + bt + č and solving for the undetermined constant vectors ā, b, and č. help (formulas) X,(t) = help (matrices) Form the general solution x(t) = x.(t) + x,(t) and impose the initial condition to obtain the solution of the initial value problem. |- X1(t) x2(t) help (formulas) help (matrices)
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10. Find the general solution of the system of differential equations 3 -2 -2 d. X = -3 -2 -6 X dt 3 10 1 + 2tet + 3t?et + 4t°et 3 1 -3 Hint: The characteristic polymomial of the coefficient matrix is -(A- 4)²(A- 3). Moreover (:) 2 1 Xp(t) = t²et +t³et +t'e3t -1 -1 -3 is a particular solution of the system.
The function of two variables ƒ(x, y) = 3x² – 2xy − 10x + y² + 2y +9 has a stationary point at (2, 1). At this stationary point, the Hessian matrix for fis H=[6₂ -2 Select the option that describes this stationary point. Select one: 2]. -2 The stationary point is a saddle point. The nature of the stationary point cannot be determined from the Hessian matrix. The stationary point is a local maximum. The stationary point is a local minimum.
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Consider a disease that propagates according to the system dx 357 — Зху — 3х dt dy = x²y – 13xy – 68y dt where X represents susceptible individuals and y represents infected individuals. (a) Find all biologically meaningful equilibria. (b) Show that J(x, y), the Jacobian matrix of this system, is given by | -3y – 3 -3x J = 2ху — 13у х2 — 13х (c) For each of the biologically meaningful equilibria from (a), find the eigenvalues of the Jacobian matrix.

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(A Find the solution of the initial value problems - Y,t Syz y. (0) = 0 92 y, + yz y z(0) ニ 2. (: ) whue the associated matrix of the system iJ: