If the given solutions ÿ₁ (t) = 2e³-8e-1 3e3-20e-t form a fundamental set (i.e., linearly independent set) of solutions for the initial value problem ÿ₂(t) = ÿ(t) = (0) 8e³+2e-t [12e³t+5e-t] ÿ, ÿ(0) = [1]. impose the given initial condition and find the unique solution to the initial value problem. If the given solutions do not form a fundamental set, enter NONE in all of the answer blanks. 2e3-8e-17 [ 3e ³ = 20e-1] + (0) 8e³+2e7 12est +5e7 1
If the given solutions ÿ₁ (t) = 2e³-8e-1 3e3-20e-t form a fundamental set (i.e., linearly independent set) of solutions for the initial value problem ÿ₂(t) = ÿ(t) = (0) 8e³+2e-t [12e³t+5e-t] ÿ, ÿ(0) = [1]. impose the given initial condition and find the unique solution to the initial value problem. If the given solutions do not form a fundamental set, enter NONE in all of the answer blanks. 2e3-8e-17 [ 3e ³ = 20e-1] + (0) 8e³+2e7 12est +5e7 1
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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![This is the fourth part of a four-part problem.
If the given solutions
ÿ₁ (t) =
2e³t 8e
3est 20e-t
form a fundamental set (i.e., linearly independent set) of solutions for the initial value problem
ÿ' =
2 (t) =
ÿ, 7(0) =
=
2e³8e-
3e320e-t
8e³+2e7
12e³t+5e7
[17],
impose the given initial condition and find the unique solution to the initial value problem. If the given solutions do not form a fundamental set, enter NONE in all of the answer blanks.
8e³+2e-
-O [12³ + 5e-²
g(t)=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ad229d2-94c2-4360-b0ca-273c76ee826c%2Fe6e3f740-cfcb-4bbe-8ae6-c4d255bf11e0%2F6nedqy_processed.png&w=3840&q=75)
Transcribed Image Text:This is the fourth part of a four-part problem.
If the given solutions
ÿ₁ (t) =
2e³t 8e
3est 20e-t
form a fundamental set (i.e., linearly independent set) of solutions for the initial value problem
ÿ' =
2 (t) =
ÿ, 7(0) =
=
2e³8e-
3e320e-t
8e³+2e7
12e³t+5e7
[17],
impose the given initial condition and find the unique solution to the initial value problem. If the given solutions do not form a fundamental set, enter NONE in all of the answer blanks.
8e³+2e-
-O [12³ + 5e-²
g(t)=
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