# What is Difference equation: Definition and 97 Discussions

In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given; each further term of the sequence or array is defined as a function of the preceding terms.
The term difference equation sometimes (and for the purposes of this article) refers to a specific type of recurrence relation. However, "difference equation" is frequently used to refer to any recurrence relation.

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1. ### I Explanation of all "its linearly independent derivatives"

I'm studying Differential Equations from Tenenbaum's, and currently going through non-homogeneous second order linear differential equations with constant coefficients. Method of Undetermined Coefficients is the concerned topic here. I will put forth my doubt through an example. Let's say we are...
2. ### I General solution of heat equation?

We know $$K(x,t) = \frac{1}{\sqrt{4\pi t}}\exp(-\frac{x^2}{4t})$$ is a solution to the heat equation: $$\frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2}$$ I would like to ask how to prove: $$u(x,t) = \int_{-\infty}^{\infty} K(x-y,t)f(y)dy$$ is also the solution to...
3. ### Engineering Finding Impulse Response of Difference Equation

And really that's all I know how to do myself. If someone can explain/lead me through this, that will be very helpful. Thanks
4. ### Boundary value problem- Random Walker

I want to solve this using difference equation. So I set up the general equation to be Pi = 0.5 Pi+1 + 0.5 i-1 I changed it to euler's form pi = z 0.5z2-z+0.5 = 0 z = 1 since z is a repeated real root I set up general formula Pn = A(1)n+B(1)n then P0 = A = 1 PN = A+BN = 0 -> A= -BN...
5. ### I Connecting wave equation with a non-constant force only in bounds

Hi hi, I'm confused about how to mix this two concepts, actually the wave equation: ##\frac {\partial^2 u} {\partial t^2} = v_x^2 \frac {\partial^2 u} {\partial x^2} + v_y^2\frac {\partial^2 u} {\partial y^2} + force## The equation will apply the rule all over the space, but I have the next...
6. ### Engineering What is the difference equation of the system?

Hey guys, what is the difference equation of the signl seen in the figure ? my suggestion is: y(k) = 2u(k) + 2u(k-1) + 2u(k-2) - y(k-6)
7. ### Engineering Z-transform of this Logistic Difference Equation

Hi, I am trying to work out how I could obtain an expression for a z-transform for the following expression: x_{n + 1} = r x_{n} \left( 1 - x_{n} \right) I am hoping to derive X(z) and then use the final value theorem to show agreement with numerically calculated steady state values. I...
8. ### Differential equation for the simple pendulum

How do I start this? I plugged the differential equation at wolfram alpha and it semmed too complicated for such an exercise. I've also looked at a sample of an answer on cheeg where the initial approach is to rewrite the equation as ##\frac{d}{dt} (\frac{\dot\theta^2}{2}-cos(\theta)) = 0## How...
9. ### Solving a Second-Order Nonlinear Differential Equation

Homework Statement Hi, I'm trying to calculate the formula for the position vs. time of a rocket landing from an altitude of 100km. I'm neglecting a lot of forces for simplification but basically, I want to solve ##F_{net} = Drag - mg##. Homework Equations Drag Force: D = ## \frac {C_dAρv^2}...
10. ### A Differential Equation to Difference Equation

Hi all, I am a bit new in this, am trying to learn DE, dynamical systems, & chaos. I am looking into some answers for the following questions: 1) Is it always possible to derive a difference equation for every differential equation, and if so how do we do that? 2) Consider Lorenz system...
11. ### Transform Dirichlet condition into mixed boundary condition

Hello, If I have a homgeneous linear differential equation like this one (or any other eq): $$y''(x)-y'(x)=0$$ And they give me these Dirichlet boundary conditions: $$y(0)=y(1)=0$$ Can I transform them into a mixed boundary conditions?: $$y(0)=y'(1)=0$$ I tried solving the equation, derivating...
12. ### What's the difference between pushing/lifting a weight?

Hi, I am working on a project where the normal process has been to push a single linear plain away from a given area. I am now considering lifting the single linear plain away but wondered about the physical dynamics when comparing pushing to lifting something. In the image:- A. Represents...
13. ### 2nd-order Nonhomogeneous Differential Equation

Homework Statement Finding the general solution: y”+4y’+4y=t*e^(-2t) Homework EquationsThe Attempt at a Solution So I got the complementary solution pretty easily as y= c1*e^(-2t)+c2*te^(-2t) I haven’t been able to find a particular solution using the method of undetermined coefficients. I...
14. ### (possible) Alternative solution to a difference equation

Hi, I'm a high school graduate who's been going through some UNISA (University of South Africa) mathematical modelling material and I've come across the following difference equation - a(n+1) = 1 - a(n). The answer given in the material was that the solution alternates between a(0) for n even...
15. ### Extending function to determine Fourier series

In the following question I need to find the Fourier cosine series of the triangular wave formed by extending the function f(x) as a periodic function of period 2 $$f(x) = \begin{cases} 1+x,& -1\leq x \leq 0\\ 1-x, & 0\leq x \leq 1\\\end{cases}$$ I just have a few questions then I will be able...

26. ### Difference equation my answer different from books

Homework Statement When drugs are used to treat a medical condition, doctors often recommend starting with a higher dose on the first day than on subsequent days. In this problem, we consider a simple model to understand why. Assume that the human body is a tank of blood and that drugs...
27. ### Difference Equation Bank Account Problem

Homework Statement Homework Equations The equation describing the balance will be f(n+1)=f(n)+R/12*Dm-Cf with f(n)=initial deposit R=Annual Rate Dm=Each mouth Deposit 150 Cf= each month fee The Attempt at a Solution Can someone shed some lights on it? Thanks[/B]
28. ### MHB Analyzing a Difference Equation

Hello! I started to study a differential equation, and turned the problem into a difference equation (a_0, a_1 \in \mathbb{R}, a_2 = 0, a_3 = \frac{a_0 + a_1}{6}) a_{v+2} = \frac{v^2a_v + a_{v-1}}{(v+1)(v+2)}, where v \ge 2. The numbers a_v are coefficients of a serie solution to the original...
29. ### How to prepare for differential equations?

I'm pretty rusty at calculus. I did well in them, but my memory is terrible and I have forgotten a lot. I'm going to take ordinary differential equations (it looks and sounds like an intro DE class with some linear algebra too) next spring. What should I study and what not to prepare for this...
30. ### Solve Difference Equation: ΔP = e^P

I have a difference equation which is given as: ΔP = e^P [1] where we can re-write ΔP as: Δ P = P_2 - P_1, where the subscripts indicate two distinct discrete time indices. What I would like to do: is to convert this into a continuous time expression and solve it, if possible. In order...
31. ### Difference equation and diagonal block matrix

Homework Statement Compute ##A^j~\text{for} ~~j=1,2,...,n## for the block diagonal matrix##A=\begin{bmatrix} J_2(1)& \\ &J_3(0) \end{bmatrix}##, And show that the difference equation ##x_{j+1}=Ax_{j}## has a solution satisfying ##|x_{j}|\rightarrow\infty~\text{as}~j\rightarrow\infty##...
32. ### Change of Variable With Legendre Equation

Homework Statement [/B] Change the independent variable from x to θ by x=cosθ and show that the Legendre equation (1-x^2)(d^2y/dx^2)-2x(dy/dx)+2y=0 becomes (d^2/dθ^2)+cotθ(dy/dθ)+2y=0 2. Homework Equations The Attempt at a Solution [/B] I did get the exact form of what the equation...
33. ### Separable differential equations

Homework Statement [/B]Homework Equations The Attempt at a Solution I've highlighted two equations on the screenshot. How did it proceed from the first to the second? I'm actually confused with the absolute values. What is the idea behind getting rid of the first absolute value(1-5v^2) while...
34. ### Difference equation solution

Homework Statement Given the following difference equation; x(k+2)-x(k+1)+0.25x(k)=u(k+2) where x(0)=1; x(1)=2; u(k)= 1 for k=1,2,3,… Homework Equations Z- transformation The Attempt at a Solution To be able to solve this difference equation, I think I need to transform it into z domain...
35. ### This is regarding difference equations and their solutions

This is regarding difference equations and their solutions. And to be specific, this is about linear constant coefficient difference equations. I read at one place, that the general solution of it can be expressed as sum of homogeneous equation and the particular solution. And at another place...
36. ### MHB Laplace transform of the integral of a difference equation

Hi, Please I need some help, how can I get the Laplace transform of the integration of a difference equation?? $\int _{ 0 }^{ \infty }{ { e }^{ -st } } \int _{ -\tau }^{ 0 }{ G(\theta )x(t+\theta )d\theta } dt$ Many thanks in advanced.
37. ### MATLAB Model a circle using finite difference equation in matlab

hello. I have a MATLAB skeleton provided because i want to model a distribution with a circular geometry. all in all, i want the 3d graph of the code to be some type of cylinder. This is the code: % flat step condition for ii=1:nHi, for jj=1:nHj, if (X(ii)/R_P)<1 &...
38. ### MHB Solve Inhomogeneous Linear Diff Eq: Zizi’s Question @ Yahoo Answers

Here is the question: I have posted a link there to this thread so the OP can view my work.
39. ### How to get (frequency response) from this [difference equation]?

Homework Statement Given this difference equation y(k) (of a bandpass FIR filter) ... y(k) = \frac{1}{K^2} \sum_{m = k-K+1}^k \; \sum_{n = m-K+1}^m x(n) - \frac{1}{L^2} \sum_{m = k-L+1}^k \; \sum_{n = m-L+1}^m x(n) ... how does one derive this frequency response H(f)? H(f) = \frac{1}{K^2}...
40. ### Convert differential equation to finite difference equation

I have the differential equation \frac{dM}{dt}=4\pi \rho(r,t)r(t)^2\frac{dr}{dt} which is the first term from M(t)=4\pi\int_0^{r(t)}C(r,t)r(t)^2dr This describes the change in mass (M) of a sphere from a change in radius (r) given a density (rho) that depends on radius and time (t). My...
41. ### Non-linear difference equation transformation

Homework Statement The problem is tough to type out correctly. Pasting problem statement image http://postimg.org/image/a0r92a0wl/ http://postimg.org/image/a0r92a0wl/ The Attempt at a Solution I just need to know how to proceed with the problem. Not the answer. This is the scan...
42. ### Solve the difference equation?

Solve the difference equation yn+1=sqrt((n+3)/(n+1)) yn in terms of the initial value y0. y1=sqrt(3)y0 y2=sqrt(6)y0 yn=sqrt(3n)y0 But that's not the answer. The answer in the textbook is yn=y0sqrt(((n+2)(n+1))/2). Did I do something wrong?
43. ### Solve the difference equation?

Solve the difference equation yn+1=(n+1)/(n+2) yn in terms of the initial value y0.
44. ### Solve the difference equation?

Solve the difference equation yn+1=-0.9yn in terms of the initial value y0. y1=-0.9y0 y2=-0.9y1=(-0.9)2y0 yn=(-0.9)ny0 Is this the answer? Because the answer in the textbook says yn=(-1)n(0.9)ny0. Please help.
45. ### Trying to understand difference equation

Hello, I hope someone can help me with a problem I am having. It is neither homework or coursework, but for my own understanding. I should say from the start, I am one of those people who tend not to be able to see the forset because all the trees are in the way, so I probably will be...
46. ### Voltage Difference Equation Terminology

For the formula for getting voltage difference V_b-V_a=-\int _a^{b} Edl how do we know where the limit a and b go? In the equation it goes from a to b but why not b to a? For example , in this question I am given a non uniform charge density where charge density increases with radius r for a...
47. ### Difference equation for interest and bank account

Homework Statement Consider your bank offers a 2% annual interest rate, and has no annual service charge. Let y[n] represent your account balance at the beginning of the month n and x[n] represent the amount of money you deposit during the month n. Assume that deposits during month n are...
48. ### Digital Filter Equivalence in a difference equation form

Homework Statement Find the digital filter equivalence of the circuit in a difference equation formHomework Equations Is this the difference equation form?The Attempt at a Solution If that is the proper form.. I think this is how to solve it? I got this example from my textbook I'm just not...
49. ### Difference Equation Coefficients

Homework Statement Work out the correct coefficient arrays for these equations: y(n)=y(n-1)+\frac{1}{5}(x(n)-x(n-5)) y(n) = 0.82y(n -1) + .28x(n) Homework Equations \sum a(r)y(n+1-r)=\sum b(k)y(n+1-k) where a(1) = 1  The Attempt at a Solution Ok for the second equation...
50. ### MATLAB Matlab Difference Equation Loop?

Trying to make a three line loop that would differentiate x2√4x+1 to the nth term starting from the original function (n=0) to the 5th derivative (n=5) and then substitute 2 into the derivatives. Here's what I got f = @(x) x2√4x+1 For n=[0:5] - As the nth term goes from 0 to 5...