) Consider the initial value problemy'1ý, y(0) =a. Find the eigenvalue A, an eigenvector i1, and a generalized eigenvector vz for the coefficient matrix of this linear system.1A = -6v1 =1b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers.ý(t) = c1+ c2c. Solve the original initial value problem.Y1(t) = |Y2(t) =

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Consider the initial value problem i' = y, j(0) = a. Find the eigenvalue A, an eigenvector i1, and a generalized eigenvector v, for the coefficient matrix of this linear system. 1 1 A= -6 v1 = ,V2 = 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. ý(t) = C1 c. Solve the original initial value problem. Y1 (t) = || Y2(t)

Consider the initial value problem i' = y, j(0) = a. Find the eigenvalue A, an eigenvector i1, and a generalized eigenvector v, for the coefficient matrix of this linear system. 1 1 A= -6 v1 = ,V2 = 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. ý(t) = C1 c. Solve the original initial value problem. Y1 (t) = || Y2(t)

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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Question

) Consider the initial value problem
y'
1
ý, y(0) =
a. Find the eigenvalue A, an eigenvector i1, and a generalized eigenvector vz for the coefficient matrix of this linear system.
1
A = -6
v1 =
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.
ý(t) = c1
+ c2
c. Solve the original initial value problem.
Y1(t) = |
Y2(t) =

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