dy = 3x – Y dt dx 4x + 2y, dt (i) Show that x(t) = 10e5t –- e-2t and y(t) = 5e5t + 3e2t form a solution (ii) Rewrite the solution in (i) in the form Y(t) = (8) = e^itv1 + e*stv2 x(t) y(t) please note that you do not need to compute eigenvalues and eigenvec- tors, just rewrite what is given in (i) (iii) Find Y(0)
dy = 3x – Y dt dx 4x + 2y, dt (i) Show that x(t) = 10e5t –- e-2t and y(t) = 5e5t + 3e2t form a solution (ii) Rewrite the solution in (i) in the form Y(t) = (8) = e^itv1 + e*stv2 x(t) y(t) please note that you do not need to compute eigenvalues and eigenvec- tors, just rewrite what is given in (i) (iii) Find Y(0)
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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Question
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Consider the system of linear
Transcribed Image Text:dy
= 3x – Y
dt
dx
4x + 2y,
dt
(i) Show that x(t) = 10e5t –- e-2t and y(t) = 5e5t + 3e2t form a solution
(ii) Rewrite the solution in (i) in the form Y(t) = (8) = e^itv1 + e*stv2
x(t)
y(t)
please note that you do not need to compute eigenvalues and eigenvec-
tors, just rewrite what is given in (i)
(iii) Find Y(0)
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