Find the solution to the following linear, homogeneous recurrence with constant coefficients: an = +2an-1 16an-2+32an-3 for n ≥ 3 with initial conditions a -13, a₁ = -30, a2 = 148. The solution is of the form: an = (a + iß)(ir)" + (a-iß)(-ir)" + ys" for suitable integer constants a, B, 7, 7, s. Note that the variable r in this problem doesn't represent a characteristic value. Find these constants and enter their values: T= 8= a = B= Y = The solution can also be written in piecewise form and purely in terms of real numbers: (Gr + cs C₂+Cs C3 +₂8 Gr + cs for suitable real constants C₁, C₂, C3, C4, C5. Find these constants as well. C₁ = C₂= C3= C₁ = C5 an= ▬▬▬▬▬▬▬▬▬▬▬▬ for n mod 4 = 0 for n mod 41 for n mod 4 = 2 for n mod 43
Find the solution to the following linear, homogeneous recurrence with constant coefficients: an = +2an-1 16an-2+32an-3 for n ≥ 3 with initial conditions a -13, a₁ = -30, a2 = 148. The solution is of the form: an = (a + iß)(ir)" + (a-iß)(-ir)" + ys" for suitable integer constants a, B, 7, 7, s. Note that the variable r in this problem doesn't represent a characteristic value. Find these constants and enter their values: T= 8= a = B= Y = The solution can also be written in piecewise form and purely in terms of real numbers: (Gr + cs C₂+Cs C3 +₂8 Gr + cs for suitable real constants C₁, C₂, C3, C4, C5. Find these constants as well. C₁ = C₂= C3= C₁ = C5 an= ▬▬▬▬▬▬▬▬▬▬▬▬ for n mod 4 = 0 for n mod 41 for n mod 4 = 2 for n mod 43
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 = +2an-1-16an-2+32an-3 for n ≥ 3 with initial conditions ao = -13, a₁ = −30, a₂ = 148. The solution is of the form:
an= (a + iß)(ir)" + (a-iß)(-ir)" +7s"
for suitable integer constants a, B,y,r, s. Note that the variable r in this problem doesn't represent a characteristic value. Find these constants and enter their
values:
T=
S=
α =
B=
Y =
The solution can also be written in piecewise form and purely in terms of real numbers:
(C₁+Cs
C₂+Cs
C3+Cs
C₁¹ +Gs
an =
for suitable real constants C₁, C₂, C3, C4, C5. Find these constants as well.
C₁ =
C₂ =
C3 =
C₁ =
C5=
for n mod 4 0
for n mod 4 1
for n mod 42
for n mod 4 = 3
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