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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
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+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
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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