Consider the initial value problem 70) - -6 1 -6 a. Find the eigenvalue A, an eigenvector õ, and a generalized eigenvector īg for the coefficient matrix of this linear system. d = -6 b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. e^(-6t) (t+1)e^(-6t) T(t) = c1 + c2 e^(-6t) c. Solve the original initial value problem. Y1 (t) = 2(t) = e^(-6t)

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the initial value problem
-6
70) =
-6
a. Find the eigenvalue A, an eigenvector 1, and a generalized eigenvector v, for the coefficient matrix of this linear system.
1
-6
1
b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers.
e^(-6t)
(t+1)e^(-6t)
ý(t) = c1
+ c2
e^(-6t)
c. Solve the original initial value problem.
Y1(t)
2(t) =
e^(-6t)
Transcribed Image Text:Consider the initial value problem -6 70) = -6 a. Find the eigenvalue A, an eigenvector 1, and a generalized eigenvector v, for the coefficient matrix of this linear system. 1 -6 1 b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. e^(-6t) (t+1)e^(-6t) ý(t) = c1 + c2 e^(-6t) c. Solve the original initial value problem. Y1(t) 2(t) = e^(-6t)
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