Find the solution to the following linear, homogeneous recurrence with constant coefficients: an= -9an-2 for n ≥ 2 with initial conditions ao = 6, a₁ = = -30. The solution is of the form: an = (a + iß) (ir)¹ + (a − iß)(−ir)" for suitable real constants a, ß, r. Note that the variable in this problem doesn't represent a characteristic value. Find these constants and enter values: ↑ = α = The solution can also be written in piecewise form and purely in terms of real numbers: for n mod 4 = 0 for n mod 4 = 1 for n mod 4 = 2 for n mod 4 = 3 Ĵ || $ C4 || an for suitable real constants C₁, C2, C3, C4. Find these constants as well. C1 = || || cir, Cyph C3p² Carn
Find the solution to the following linear, homogeneous recurrence with constant coefficients: an= -9an-2 for n ≥ 2 with initial conditions ao = 6, a₁ = = -30. The solution is of the form: an = (a + iß) (ir)¹ + (a − iß)(−ir)" for suitable real constants a, ß, r. Note that the variable in this problem doesn't represent a characteristic value. Find these constants and enter values: ↑ = α = The solution can also be written in piecewise form and purely in terms of real numbers: for n mod 4 = 0 for n mod 4 = 1 for n mod 4 = 2 for n mod 4 = 3 Ĵ || $ C4 || an for suitable real constants C₁, C2, C3, C4. Find these constants as well. C1 = || || cir, Cyph C3p² Carn
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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Transcribed Image Text:Find the solution to the following linear, homogeneous recurrence with constant coefficients:
an = -9an-2 for n ≥ 2 with initial conditions ao = 6, a₁ = -30. The solution is of the form:
an = (a + iß)(ir)" + (a − iß)(-ir)"
for suitable real constants a, ß, r. Note that the variable r in this problem doesn't represent a characteristic value. Find these constants and enter their
values:
r =
a =
B =
The solution can also be written in piecewise form and purely in terms of real numbers:
C₂ =
C3 =
for suitable real constants C₁, C2, C3, C4. Find these constants as well.
C₁ =
C4 =
TI
an =
C
(C₁,
Cyph
C3p
Carn
for n mod 4 = 0
for n mod 4 = 1
for n mod 4 = 2
for n mod 4 = 3
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