Question: Consider the recurrence xk+2 = axk+1 + bxk + c(k) (*) where c(k) is a function of k, and consider the related recurrence xk+2 =

Consider the recurrence
xk+2 = axk+1 + bxk + c(k) (*)
where c(k) is a function of k, and consider the related recurrence
xk+2 = axk+1 + bxk (**)
Suppose that xk = pk is a particular solution of (*).
(a) If qk is any solution of (**), show that qk + pk is a solution of (*).
(b) Show that every solution of (*) arises as in (a) as the sum of a solution of (**) plus the particular solution pk of (*).

Step by Step Solution

★★★★★

3.36 Rating (149 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a If p k is a solution of and q k is a solution of then q k2 aq k1 bq k p k2 ap k1 bp k ck f... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

950-M-L-A-L-S (6351).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Knowing that the tension in wire BD is 300 lb, determine the reaction at fixed support C for the frame shown. 180 Ib 6 in. 10 in. -20 in. 100 lb 24 in. 16 in.

Consider the recurrence xk+2 = axk+1 + bxk + c where c may not be zero. (a) If a + b 1 show that p can be found such that, if we set yk = xk + p, then yk+2 = ayk+1 + byk. [Hence, the sequence xk can...

The semi perimeters of regular polygons with k sides that inscribe and circumscribe the unit circle were used by Archimedes before 200 b.c.e. to approximate , the circumference of a semicircle....

In this exercise we briefly introduce the Master Theorem. (For more on this result, including a proof, we refer the reader to pp. 73-84 of reference [5] by T. H. Cormen, C. E. Leiserson, R. L....

CS208 WK3 QUIZ 1 1. Given x0 = 2, xn = 2xn1 - 3, and n > 1. What is the value of x3 ? x0 = 2 x1 = 2(2) - 3 = 1 x2 = 2 x 2(2)] - 3 = 1 x3 = 2[2 x 2(2)] - 3 = 5 2. Given S0 = 1, S1 = 2, Sn = 2Sn1 +...

Can somebody please go through these questions? Consider a recursion tree that looks like this: n2 (n/22 (n/2) (n/2) (14)* (14) (14) (1/4)2 (1/4) (/4) (1/4) (14) (1/4)* 1. Suppose this tree is...

(31 points) Suppose you are given k sorted non-empty lists A_(1),dots,A_(k) that consist of n elements in total. Your task is to merge them into one big sorted list. We will use the merge procedure...

(1) a) What is (3/4) ? b) What is the Li-2 i(3/4)*? A coin has 1/4 chance of having heads, 3/4 chance of having tails. It is tossed n times. a) What is the expected number of coin tosses needed to...

13 continued: . PLEASE ANSWER 9 THROUGH 13!!!!!!!!!!!! --------------------------- 9. Consider the recurrence T(n) = sqrt(2)T(n/2)+lg n. a. Which case of the Master method can we use to solve the...

1. Consider the following recurrence. T(n)= T([n/2]) +27([n/8])+n n>8, and T(n)=1 15n 0. Consider the recurrence T(n)= T(Lcn])+ T(Lc2n])+T([czn])+an, n> 1/c,T(n)=1 ns1/c1. = Prove by induction that...

Consider the following recurrence relation H(n) = {0 if n lessthanorequalto 0 1 if n = 1 or n = 2 H(n - 1) + H(n - 2) - H (n - 3) if n > 2. (a) Compute H(n) for n = 1, 2, ..., 10. (b) Using the...

A spherical shell, of radius R, carrying a uniform surface charge o, is set spinning at angular velocity w(t). Find the vector potential it produces at point x as

Suppose that in Exercise 9-25 we wanted to reject the null hypothesis with probability at least 0.8 if mean strength = 3500. What sample size should be used?

evaluate indefinite integral ( 2 4 sec ^ - 1 ( 3 x ) / ( xsqrt ( 9 x ^ 2 - 1 ) ) ) dx

Consider a system consisting of four resources of the same type that are shared by three processes, each of which needs at most two resources. Show that the system is deadlock free.

Among the ways in which 1, 4-dioxane may be prepared are the methods expressed in the equations shown:

When (R)-(+)-2-phenyl-2-butanol is allowed to stand in methanol containing a few drops of sulfuric acid; racemic 2-methoxy-2-phenylbutane is formed. Suggest a reasonable mechanism for this reaction.

The interest rate is 16%per year and there are 48 compounding periods per year. The principal is $50,000. What is the future worth in 5 years?

Combine Probs. 112 and 113 for an overall reliability of R = 0.90. Reconsider your selections, and meet this overall reliability goal.

A lobby group suggests a constitutional amendment to the effect that government budgets must be balanced, arguing that allowing politicians discretionary power leads to large deficits and escalating...

Show that if ad - bc 0, then the reduced row-echelon form of 1 1

Indicate all possible reduced row-echelon forms of (a) (b) be adg

Indicate whether the statement is always true or sometimes false. Justify your answer by giving a logical argument or a counterexample. (a) If a matrix is reduced to reduced row-echelon form by two...

Thank you so much Listed below are amounts of court income and salaries paid to the town justices. All amounts are in thousands of dollars. Construct a scatterplot, find the value of the linear...

Treasury Bonds Ask Bid 8 May 00-05 101-8/32 101-4/32 12 May 05 129-29/32 129-23/32 8 7/8 May 00 104-16/32 104-12/32 Treasury Strips May 00 46-21/32 46-08/32 May 05 30-10/32 29-29/32 Consider an...

Q1 The table below indicate the norm for students grades in MGSC 301. Grade Excellent Very Good Good Accepted Fail Proportion of Students 0.4 0.3 0.15 0.1 0.05 Q1 The new cohort of 75 students in...