Given the vector functions [-2₂2²]e ²7 e-t are solutions to a 2 x 2 constant-coefficient differential system, a) compute the Wronkskian of {y₁, №2}. W(t) = У1 = b) Are {y₁, y2} are linearly independent? and Y2 O Yes, {y₁, y2} are linearly independent. O No, {y1, y2} are linearly dependent. Y(t) = = c) Determine the fundamental matrix of the system. 5 [₁] e 4t

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Given the vector functions
=
У1
=
Y(t)
2
e
=
t
are solutions to a 2 × 2 constant-coefficient differential system,
a) compute the Wronkskian of {y₁, №2}.
W(t)
b) Are {y₁, y2} are linearly independent?
and Y2
O Yes, {y1, 2} are linearly independent.
O No, {y1, y2} are linearly dependent.
=
c) Determine the fundamental matrix of the system.
4t
Transcribed Image Text:Given the vector functions = У1 = Y(t) 2 e = t are solutions to a 2 × 2 constant-coefficient differential system, a) compute the Wronkskian of {y₁, №2}. W(t) b) Are {y₁, y2} are linearly independent? and Y2 O Yes, {y1, 2} are linearly independent. O No, {y1, y2} are linearly dependent. = c) Determine the fundamental matrix of the system. 4t
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