This is the third part of a four-part problem. If the given solutions ₁ (t) = 2e³t 3e³t+15e7 yı(t) +60-1], 5₂(t) = Y2 (t) form a fundamental set (i.e., linearly independent set) of solutions for the system -4 -7 ÿ' = [1 9 - [4e³t+2e= 3t +5e-t ÿ, 6e3t 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) = y(t) č, where (t) is a square matrix whose columns are the solutions forming the fundamental set and è is a column vector of arbitrary constants. 1 [8]] = C1 C2
This is the third part of a four-part problem. If the given solutions ₁ (t) = 2e³t 3e³t+15e7 yı(t) +60-1], 5₂(t) = Y2 (t) form a fundamental set (i.e., linearly independent set) of solutions for the system -4 -7 ÿ' = [1 9 - [4e³t+2e= 3t +5e-t ÿ, 6e3t 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) = y(t) č, where (t) is a square matrix whose columns are the solutions forming the fundamental set and è is a column vector of arbitrary constants. 1 [8]] = C1 C2
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 third part of a four-part problem.
If the given solutions
ÿ₁ (t) =
2e³t
3e³t+15e7
+60-1], 5₂(t) =
yı(t)
Y₂(t)
form a fundamental set (i.e., linearly independent set) of solutions for the system
9 -4
ÿ' = [₁
[15
-7
-
[4e³t+2e=
3t
+5e-t
ÿ,
6e3t
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) = Y(t)ẻ, where (t) is a square matrix whose columns are the solutions forming
the fundamental set and è is a column vector of arbitrary constants.
1 [8]]
=
C1
C2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6890296c-2fc0-4a83-b66a-ee1a85d807a1%2Fd55d8706-8db5-4182-aa76-2e1d726270fd%2Fztyup9f_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
3e³t+15e7
+60-1], 5₂(t) =
yı(t)
Y₂(t)
form a fundamental set (i.e., linearly independent set) of solutions for the system
9 -4
ÿ' = [₁
[15
-7
-
[4e³t+2e=
3t
+5e-t
ÿ,
6e3t
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) = Y(t)ẻ, where (t) is a square matrix whose columns are the solutions forming
the fundamental set and è is a column vector of arbitrary constants.
1 [8]]
=
C1
C2
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