Consider the linear system -3 a. Find the eigenvalues and eigenvectors for the coefficient matrix. -3+i -3-i d1 = i , v1 = , and A2 = -i U2 = b. Find the real-valued solution to the initial value problem —Зул — 2у2, Y1(0) = -1, 5y1 + 3y2, Y2(0) = 5. %3D Use t as the independent variable in your answers. Y1(t) Y2(t)

Consider the linear system -3 a. Find the eigenvalues and eigenvectors for the coefficient matrix. -3+i -3-i d1 = i , v1 = , and A2 = -i U2 = b. Find the real-valued solution to the initial value problem —Зул — 2у2, Y1(0) = -1, 5y1 + 3y2, Y2(0) = 5. %3D Use t as the independent variable in your answers. 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 linear system

y→′=[−3−253]y→.

Find the eigenvalues and eigenvectors for the coefficient matrix.

λ1= , v→1=

[ ]

, and λ2= , v→2=

[ ]
Find the real-valued solution to the initial value problem
{y1′=−3y1−2y2,y1(0)=−1,y2′=5y1+3y2,y2(0)=5.
Use t as the independent variable in your answers.

y1(t)=
y2(t)=

Consider the linear system
j' =
j.
a. Find the eigenvalues and eigenvectors for the coefficient matrix.
-3+i
-3-i
A1 = i
v1 =
, and A, =
-i
v2 =
5
b. Find the real-valued solution to the initial value problem
— Зул — 2у2,
5y1 + 3y2,
ул (0) — —1,
Y2(0) = 5.
Use t as the independent variable in your answers.
Y1(t)
Y2(t)
||||

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