b) If the Wronskian at t = 1 is 5 d³y dt³ d'y dt4 d³y dt3 - t- (1) = 1 d²y dt² -t². d²y dt.² dy 13. dt - t4y = 7 cos (t) dy (1) = 1 (1) = 2 y(1) = 9 dt

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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b) W(1) = 5, what is W(t)? 

7. Write the 4th order ordinary differential equation as a matrix system of first order ordinary
differential equations with an initial vector condition.
& indicate what the terms A, X. X, and g(t) are.
a) in the form x Ax+s(t) withx{1}
b) If the Wronskian at t = 1 is 5
day
dt4
d³y
dt3
t
d³y
dt 3
(1) = 1
d²y
dt²
1².
d²y
dt²
-
t3
(1) = 1
dy
dt
dy
dt
t4y = 7 cos (t)
(1) = 2 y(1) 9
Transcribed Image Text:7. Write the 4th order ordinary differential equation as a matrix system of first order ordinary differential equations with an initial vector condition. & indicate what the terms A, X. X, and g(t) are. a) in the form x Ax+s(t) withx{1} b) If the Wronskian at t = 1 is 5 day dt4 d³y dt3 t d³y dt 3 (1) = 1 d²y dt² 1². d²y dt² - t3 (1) = 1 dy dt dy dt t4y = 7 cos (t) (1) = 2 y(1) 9
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