Transform the the second-order initial-value problemy" + y – 6y' = 0, for 0 < t < 1, with y (0) = -1, y (0) = 6into a system of first order initial-value problems, and use the Runge-Kuttamethod of order 4 of systems with h = 0.2 to approximate y(0.2).Maximum file size: 100MB, maximum number of files: 1Files

Given the second order differential equation: y''+y-6y'=0 With the conditions that y0=-1 and y'0=6…

Answered: Transform the the second-order…

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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The system of non-linear differential equations x = -sin x COS Y, y = sin x + sin y, has an equilibrium point at (,0). (a) Calculate the Jacobian matrix of this system of equations and evaluate this matrix at the given equilibrium point. (b) Use your answer to part (a) to classify this equilibrium point.
This is the solution of y" + 4y' + 3y = 8 (t – 2), y (0) = 0, y' (0) = 0 O y = } [e-t-2) – e-3(t-2)] U (t – 2) O y = } [e-(t-2) – e-3(t-2)] & (t – 2) O y = [et - e-] U (t – 2) O y = [e-t-1) – e-2(t-1)] U (t – 1)
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Consider a system of differential equations X'= Ax, where X = and the 2x2 matrix A has eigenpairs 1 Vị = 1 d1 = 3, and d2 = 2, V2 V2 From the options below, find the correct behavior of the solution x(t) = -Vị e^it + v2 est. lim ||x(t)|| lim ||x(t)|| = 0, = ∞, t→-∞ x(0) = [va): x(t) x(t) lim t→0 x(t)|| V1, lim V2, t-o ||x(t)|| lim ||x(t)|| = 0, lim ||x(t)|| =∞, t→∞ t -∞ x(t) x(t) lim x(0) V2, lim V1, 00 ||x(t)|| t-0 x(t)|| lim ||x(t)|| = ∞, lim ||x(t)|| = 0, t→∞ x(0) = ,v. x(t) x(t) lim t→-0 ||x(t)|| lim V1, V2, t>0 ||x(t)|| lim ||x(t)|| = 0, lim ||x(t)|| = 0∞, t→∞

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Transform the the second-order initial-value problem y" + y −6y' = 0, for 0 < t < 1, with y (0) = -1, y' (0) = 6 into a system of first order initial-value problems, and use the Runge-Kutta method of order 4 of systems with h = 0.2 to approximate y(0.2).