This is the third part of a four-part problem. If the given solutions ÿ₁ (t) = 2e³t+6e- +15e-t [3e³t -t' ÿ' = form a fundamental set (i.e., linearly independent set) of solutions for the system -4 9 ₂(t) = 15 - 7 ÿ, [4e³t+ 2e 6e3t +5e- 1- [88 = state the general solution of the linear homogeneous system, and if they do not, enter NONE in all of the answer blanks. Express the general solution as the product ÿ(t) = (t)e, where (t) is a square matrix whose columns are the solutions forming the fundamental set and is a column vector of arbitrary constants. Yı(t) Y₂(t) C1 TE C2
This is the third part of a four-part problem. If the given solutions ÿ₁ (t) = 2e³t+6e- +15e-t [3e³t -t' ÿ' = form a fundamental set (i.e., linearly independent set) of solutions for the system -4 9 ₂(t) = 15 - 7 ÿ, [4e³t+ 2e 6e3t +5e- 1- [88 = state the general solution of the linear homogeneous system, and if they do not, enter NONE in all of the answer blanks. Express the general solution as the product ÿ(t) = (t)e, where (t) is a square matrix whose columns are the solutions forming the fundamental set and is a column vector of arbitrary constants. Yı(t) Y₂(t) C1 TE C2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![This is the third part of a four-part problem.
If the given solutions
ÿ₁ (t) =
2e³t+6e-
+15e-t
[3e³t
-t'
ÿ'
=
form a fundamental set (i.e., linearly independent set) of solutions for the system
9
₂(t) =
15
-
-
7
ÿ,
[4e³t+ 2e
[6e3t
+5e-
1-188
=
state the general solution of the linear homogeneous system, and if they do not, enter
NONE in all of the answer blanks. Express the general solution as the product
y(t) = (t)e, where (t) is a square matrix whose columns are the solutions forming
the fundamental set and is a column vector of arbitrary constants.
y₁ (t)
Y₂(t)
C1
TE
C2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6890296c-2fc0-4a83-b66a-ee1a85d807a1%2F0d47830f-0f43-4c4b-be5c-fc375959f384%2Fv76puw9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:This is the third part of a four-part problem.
If the given solutions
ÿ₁ (t) =
2e³t+6e-
+15e-t
[3e³t
-t'
ÿ'
=
form a fundamental set (i.e., linearly independent set) of solutions for the system
9
₂(t) =
15
-
-
7
ÿ,
[4e³t+ 2e
[6e3t
+5e-
1-188
=
state the general solution of the linear homogeneous system, and if they do not, enter
NONE in all of the answer blanks. Express the general solution as the product
y(t) = (t)e, where (t) is a square matrix whose columns are the solutions forming
the fundamental set and is a column vector of arbitrary constants.
y₁ (t)
Y₂(t)
C1
TE
C2
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