Odes Definition and 255 Threads

How can I use finite difference to discretize a system of fourth order differential equations? for example: y(4)+5y(3)-2y''+3y'-y=0

If you really want to know where this comes from I am solving the GR equations for a rectilinearly isotropic metric. In other words, I can express the metric as d \tau ^2 = -T(x) dt^2 + X(x) dx^2 + dy^2 + dz^2. (It may be simpler to use a cylindrical coordinate system, but the equations come...

**Background:** I have been working on this problem for my research for months now, and I am in dire need of help. That is why I have come here to seek help. I have a system of nine ODEs that describe the dynamics of HIV and Tuberculosis co-infection in a population. The disease-free...

Hello, I am in an introductory undergraduate course on ODEs, currently on the method of variation of constants to solve nonhomogenous equations. I am noticing that with many of these problems, when solving for constants after plugging in my guessed values for y I end up with enormous...

I am taking and advnaced ODEs course at uni. The first four weeks have been challenging but doable with some research outside. As we approach more special functions, it has gotten hectic and I've even fallen two weeks behind :/. Some of the questions we get are insanely scary! Our lecturer...

Hi everyone, I have searched all over the site to see if I am repeating a question, but I don't believe that I am. So I am currently in the life sciences, but I am switching to physical sciences to do a graduate degree in one year. The program, obviously, recommends that I have decent...

Homework Statement Why does the following ODE ALWAYS have two linearly independent solutions? x''(t) + a(t) x'(t) + b(t) x(t) = f(t) The characteristic polynomial argument is not sufficient?

I have an ODE ##e^{2x}H(Hv'(x) + H'v' + Hv'') + (k^2 - 2e^{2x}H^2(1 + \frac{H'}{2H}))v = 0## where ##H(x)## is a known function that Mathematica has stored as an interpolation from a previous ODE and ##v(x)## is the unknown function to be solved for. ##k## is the adjustable parameter. Using...

I want to solve for $x$ and $y$ from the equation $$\frac{dx}{dt} + \frac{dy}{dt}=a-(b+c+d)y-bx.$$ What is the best strategy?

Hi, I am just having a little trouble with differential equations. I have y'' - 6y' + λy = 0 I know I need complex roots and setting e^\alphax gives \alpha= 3+/-sqrt(9 - λ). Then I don't understand why set -ω^2= 9-λ. How do you know if it is -ω^2 or w^2. Thanks for the help.

Hello everyone, I have the following coupled ODEs (r\geq 0) g^2v^2f(r)h^2(r)+\frac{6}{r}f'(r)-3f''(r)=0, r^2h''(r)-4f^2(r)h(r)=0, with boundary conditions f(\infty)=1, h(\infty)=1. The other 2 boundary conditions are arbitrary. Also v and g are constants, that could be set to a fixed value...

I am stuck with the issue quite sometimes already. The question is to solve a 2 complex 1st order complex ODEs. The hints that given by the professor is to separate the ODEs into the real and imaginary part as ocatve/matlab only capable of handling real ODEs with “ isode “ function. So...

Hi, I have looked everywhere. Can someone please point me in the right direction for solving a system of ODEs with variable coefficients? I managed to solve such system with constant coefficients.

Questions about Green's functions for ODEs, jump conditions I'm having a hard time understanding Green's functions which have been introduced quite early on in the course, and which I think hasn't been well motivated. I can't find any other resource which explains this at this level (have only...

I have the following 2 problems to solve using Laplace. 1) x'' + 3x' +2x=e^(-t); with x=dx/dt=0 when t = 0 2) x'' - 2x' +10x=e^(2t); with x=0 and dx/dt=1 when t=0 Where x' is dx/dt and x'' is the second derivative against time. My attempts: 1)Using laplace I get...

Homework Statement Solve: [ d^2y1/dx^2 ] = [ a -a ] [ y1 ] [ d^2y2/dx^2 ] [ -a a ] [ y2 ] A = [ a -a ] [ -a a ] Homework Equations Everything required is in (1) above The Attempt at a Solution Reduce to 1st order system M = [ 0 I ] [ A 0 ] Hence, M = [ 0 0 1...

Fint the modified equation when the implicit Euler method is applied to y'= f(y). If f(y)=λy, where λ is negative. what is the effect on the amplication factor? => y ' = λ * y dy / dx = λ * y dy / y = λ dx ln y = λ* x + C y = Ae^( λ* x ), the constant factor does not depend on λ. i...

For the equation dy/dt =y(1-ky), where k is a constant,find the fixed points and investigate their stability. what are the fixed points of the modified Euler Scheme applied to this equation and what is their stability? => dy / dt = y ( 1 - ky ) dy / dt = y - ky^2 dy / dt - y = - ky^2 Let v...

Fint the modified equation when the implicit Euler method is applied to y'= f(y). If f(y)=λy, where λ is negative. what is the effect on the amplication factor? => y ' = lambda * y dy / dx = lambda * y dy / y = lambda dx ln y = lambda * x + C y = [ C / lambda ]e^( lambda * x ) This is what...

By a fortuitous mistake in copy/pasting, I happened across this system. It exhibits very chaotic behavior for some initial values and spiral-like shapes for others. (About a 70%/30% split, respectively.) x'=cosy+sint y'=sinx+cost Here's an album of it plotted from t=0 to 1000. The titles of...

In my class, I learned about a First-order ODEs, and solvable and unsolvable. example in case solvable ODEs) dy/dt=t/y dy/dt=y-t^2 example in case unsolvable ODEs) dy/dt=t-y^2 but , i don't know how distinguish those. please, teach ME! : ( as possible as easily !

Here are the questions: I have posted a link there to this thread so the OP can view my work.

Suppose I have a variable separable ODE, e.g., \frac{dy}{dx} = 3y. We all know that the solution is y=Ae^{3x} where A is a constant. My question is as follows. To actually find this solution we rearrange the equation and integrate to get \int \frac{dy}{y} = 3 \int dx, which gives \ln...

Consider the first order differential equation \[\frac{dy}{dy} = f(t,y) = -16 t^3 y^2\] with initial condition $y(0)=1$ Using second order Adams-Bashforth method, write a Fortran programming to generate an approximate solution to the problem. Solution Program adams Implicit None Real...

Consider the ODE x(x-1)y''-xy'+y=0. I need help in identifying the method of solution (power series or frobenius) for this ODE. Using the formulae \stackrel{limit}{_{x→x_{o}}}\frac{q(x)+r(x)}{p(x)} and \stackrel{limit}{_{x→x_{o}}}\frac{(x-x_{o})q(x)+(x-x_{o})^{2}r(x)}{p(x)} , where...

Given the matrix b=\begin{pmatrix}-1&0&-1\\-4&3&-1\\0&0&-2\end{pmatrix} decide if the system of ODEs, \frac{dx}{dt}=Bx is decoupled. If yes find the general solution x=xh(t) Homework Equations The Attempt at a Solution I would say the matrix is decoupled since the second equation...

Homework Statement Given the matrix b=\begin{pmatrix}-1&0&-1\\-4&3&-1\\0&0&-2\end{pmatrix} decide if the system of ODEs, \frac{dx}{dt}=Bx is decoupled. If yes find the general solution x=xh(t) Homework Equations The Attempt at a Solution I would say the matrix is decoupled since the second...

I need to know how I can prove the existence and uniqueness of a solution (using Lipschitz condition and well-posedness, stability analysis, etc.) for a system of 12 ordinary differential equations. I have the theorem that I need to use, but the number of calculations and work that I would have...

Could someone please provide a worked solution for me. I think that is the only way I will understand this. It was covered very vaguely in our lectures and my notes start talking about vectors and using co-domain notation which is very frustrating! 1. $y''(x) = x + y'(x) + e^{y(x)}$ with...

Given \(F = A(x)u_1^{'2} + B(x)u'_1u'_2 + C(x)u_2^{'2}\). \[ \frac{\partial F}{\partial u_i} - \frac{d}{dx}\left[\frac{\partial F}{\partial u_i'}\right] = 0 \] From the E-L equations, I found \begin{align*} \frac{d}{dx}\left[2Au_1' + Bu_2'\right] &= 0\\ \frac{d}{dx}\left[2Cu_2' + Bu_1'\right] &=...

Hi all, The title is pretty much the question. My friend (who wants to go to graduate school in Physics) is between two courses the math department offers: an upper-level linear algebra course, and a second course in ODEs. Here are the course descriptions: and The school in question is...

Homework Statement Solve the equations of motion ##\ddot{y}= \omega \dot{z}## and ##\ddot{z}= \omega (\frac{E}{B}-\dot{y})## Homework Equations The Attempt at a Solution Integrate the first equation to get ##\dot{y}=\omega z + c_1## and plug into equation 2: ##\ddot{z}=\omega...

Hello, I am having trouble solving the below IVP, particularly I am confused with the w: du/dt = v - w(t-5) dv/dt = 2 - u(t) u(0)=0, v(0)=0 Any help would be great. Thank you.

Here are the questions: I have posted a link there to this topic so the OP can see my work.

I need help with the following so please help me -- Consider the following non-linear system X’ = x² - ay Y’ = y² - y(a) Find the fixed points of this system. (depending on a, there may be different fixed points!) (b) Study stability of each fixed point via linearization. In the case the...

I have another question so please help me. here we go -- Consider the following linear system of ODE : X’ = -x – y Y’ = x + 3y Z’ = 4x + 6y - z Note that the matrix of this system is exactly the same as A = [ 1 -1 0 1 3 0 4 6 -1 ] (a) Study the stability of the fixed...

Here are the questions: Here is a link to the questions: HELP WITH THESE DIFFERENTIAL EQUATION? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Using the 4th-order Runge-Kutta method, I have been able to successfully compute the solutions to a coupled pair of two first order differential equations using the following formula: When solving systems of ODEs with more than two equations I am unsure if I am properly expanding on the...

Dear Fellows, I want to solve 4 differential homogeneous equations for non trivial solution. I have found two methods 1) Determinent. 2) Elimination By det. I got 8th order resultant equation and by second method I got 10th order. As each of initial equation is 2nd order so 8th is correct. But...

Homework Statement Find a particular solution to ##\begin{cases}x'=5x+4y+t\\ y'=x+8y-t\end{cases}## using a variety of methods that are listed. I've been using undetermined coefficients on this problem thus far. Homework Equations The Attempt at a Solution My answer is...

Homework Statement Suppose a cart of mass 2 kg is attached by a spring of constant k = 1 to a cart of mass 3 kg, which is attached to the wall by a spring also of k = 1. Suppose the initial position of the first cart is 1 m in the positive direction from the rest position, and the second...

Hi, I'm trying to come up with some examples of ODEs (not PDES) in physics that are unsolvable analytically, and for some reason I'm drawing a blank. There are a few obvious examples from classical mechanics such as a pendulum and coupled springs etc... but beyond that I can't seem to recall...

Homework Statement He tells us to find the form of the particular solution without having to compute the actual particular solution. For Example, (D^{2}+1)y = xe^{-x}+3sinx Homework Equations I'm not even 100% sure how to begin...I was kind of hoping someone could explain what the...

Homework Statement In my book, I'm given that ##\vec{x}_1=\left(\begin{matrix}t^2\\t\end{matrix}\right), \vec{x}_2=\left(\begin{matrix}0\\1+t\end{matrix}\right), \vec{x}_3=\left(\begin{matrix}-t^2\\1\end{matrix}\right)## are solutions. My textbook presents an algebraic way to show that the...

Homework Statement Find the general solution of the given differential equation: y''+y'+4y=2sinht Homework Equations I believe sinht=(e^t-e^-t)/2 The Attempt at a Solution I tried to find the general equation if it were homogenous however I get the roots are r=[1+-...

So, this is probably really easy, but it's been bugging me...is the following differential equation linear? e^{y'' + y} = 12 'Cause can't you just take logarithms on both sides and get it to be y'' + y = \log 12 I guess the question I'm trying to ask is...what operations are...

Homework Statement Given the attached figure, a) Develop an ordinary differential equation that describes the dynamic height h(t) in the flash tank in terms of \dot{m}_{i}, \dot{m}_{l},\dot{m}_{v}, \rho_{i}, \rho_{l}, \rho_{v}, and A. b) Given the fact that the process is isenthalpic...

It says on Wikipedia in the article on differential equations that: 'a differential equation is linear if the unknown function and its derivatives appear to the power 1 (products are not allowed) and nonlinear otherwise' Are these products between any of the variables that appear? So, are...

EDIT: Wow, just realized I skipped a crucial step. Forgot to isolate y' while I was working out the problem and now I see you can't even isolate y' without going back to the original equation. Sorry, disregard the thread please. I'm taking an introductory ODE course (I've only taken up to...

I need to solve the following ODE: http://www.sosmath.com/CBB/latexrender/pictures/041ee1419e05bc0776451b294c1dcc0e.png but i can't figure out a way to. Please help!