Find solutions to the following difference equations: • xn+2 − 4xn = 27n 2 , x0...

Find solutions to the following difference equations:

• xn+2 − 4xn = 27n 2 , x0 = 1, x1 = 3

• xn+1 − 4xn + 3xn−1 = 36n 2 , x0 = 12, x1 = 0

• xn+1 − 4xn + 3xn−1 = 3n , x0 = 2, x1 = 13/2

• xn+2 − 2xn+1 + xn = 1, x0 = 3, x1 = 6

Expert Solution

as per our guidelines, i will solve the first question only.

Colby Messinger answered 2 years ago

find the general solution of the following as follows Xn+2 = -2Xn+1 + 3Xn, x0=1 x1=2...

find the general solution of the following as follows Xn+2 = -2Xn+1 + 3Xn, x0=1 x1=2 a) find the 2x2 matrix that satisfies Yn+1=AYn b) Find the characteristic value of A and its corresponding characteristic vector c) express X0 = (1 2)as a linear combination of characteristic vector d) find Yn e) find Xn

2. Consider the stochastic process {Xn|n ≥ 0}given by X0 = 1, Xn+1 = I{Xn =...

2. Consider the stochastic process {Xn|n ≥ 0}given by X0 = 1, Xn+1 = I{Xn = 1}Un+1 + I{Xn 6= 1}Vn+1, n ≥ 0, where {(Un, Vn)|n ≥ 1} is an i.i.d. sequence of random variables such that Un is independent of Vn for each n ≥ 1 and U1−1 is Bernoulli(p) and V1−1 is Bernoulli(q) random variables. Show that {Xn|n ≥ 1} is a Markov chain and find its transition matrix. Also find P{Xn = 2}.

Find all solutions to the following equations: (a) √2x − 2 = √x + 1 (b)...

Find all solutions to the following equations: (a) √2x − 2 = √x + 1 (b) x4 − 5x2 + 6 = 0 (c) |3x − 7| < 5 (d) |ax + b| ≥ c Explain step by step please Suppose 4 is a right triangle with leg-lengths a and b and hypotenuse c. Find the missing side: (a) a = 3, b = 4, c =? (b) a = 12, c = 13, b =? (c) a = 6,...

Use the method of undetermined coefficients to find the complete solutions of the following differential equations....

Use the method of undetermined coefficients to find the complete solutions of the following differential equations. d2y/dx2 − 3 dy/dx + 2y = 2x2 + ex + 2xex + 4e3x .

Find the General Solutions to the given differential equations y(t) = a) 6y' +y = 7t^2...

Find the General Solutions to the given differential equations y(t) = a) 6y' +y = 7t^2 b) ty' − y = 9t2e−9t, t > 0 c) y' − 8y = 9et d) y' + y/t = 6 cos 5t, t > 0

Find two power series solutions of the following differential equations. y'' - xy' = 0

a. Seek power series solutions of the given differential equation about the given point x0; find...

a. Seek power series solutions of the given differential equation about the given point x0; find the recurrence relation that the coefficients must satisfy. b. Find the first four nonzero terms in each of two solutions y1 and y2 (unless the series terminates sooner). y''-xy'-y=0 ; x0=0

(a) Seek power series solutions of the given differential equation about the given point x0; find...

(a) Seek power series solutions of the given differential equation about the given point x0; find the recurrence relation. (b) Find the first four terms in each of two solutions y1 and y2 (unless the series terminates sooner). (c) By evaluating the Wronskian W(y1, y2)(x0), show that y1 and y2 form a fundamental set of solutions. (d) If possible, find the general term in each solution. 1. y''-y=0, x0=0 2. y''-xy'-y=0, x0=0 3. (4-x^2)y''+2y=0, x0=0 4. 2y''+(x+1)y'+3y=0, x0=2

NUMBER THEORY 1.Find all the possible solutions for the following diphantine equations by using the euclidian...

*NUMBER THEORY* 1.Find all the possible solutions for the following diphantine equations by using the euclidian algorithim. You must show all the process to get credit. a. 3x + 5y = 7 b. 3x − 12y = 7 c. 1990x − 173y = 11 d. 21x + 48y = 6 e. 2x + 3y + 5z = 11

Consider the following Markov chain with P{X0 = 2} = 0.6 and P{X0 = 4} =...

Consider the following Markov chain with P{X0 = 2} = 0.6 and P{X0 = 4} = 0.4: 1 2 3 4 5 6 1 0 0 0 0 1 0 2 .2 .05 0 .6 0 .15 3 0 0 .8 0 0 .2 4 0 .6 0 .2 0 .2 5 1 0 0 0 0 0 6 0 0 .7 0 0 .3 a. What is P{X1 = 4, X2 = 6 | X0 = 2}? b. What...

Question

Find solutions to the following difference equations: • xn+2 − 4xn = 27n 2 , x0...

Solutions

Expert Solution

Related Solutions