What is Odes: Definition and 254 Discussions

For a book included in some editions of the Septuagint, see The Book of Odes.The Odes of Solomon is a collection of 42 odes attributed to Solomon. Various scholars have dated the composition of these religious poems to anywhere in the range of the first three centuries AD. The original language of the Odes is thought to have been either Greek or Syriac, and to be generally Christian in background.

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  1. topsquark

    MHB Coupled non-linear system of ODEs

    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...
  2. K

    MHB Constructing Lyapunov function for system of ODEs

    **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...
  3. H

    Method of Variation of Coefficients

    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...
  4. N

    MHB Struggling with Advanced ODEs? Here's Some Guidance and Recommended Texts!

    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...
  5. R

    Learning ODEs: Self-Teaching for a Graduate Degree

    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...
  6. L

    Why do 2nd-order linear ODEs have at most two independent solutions?

    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?
  7. WannabeNewton

    Mathematica Solving ODEs with large parameters in Mathematica 9

    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...
  8. K

    MHB Solving a system of linear ODEs

    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?
  9. D

    Understanding Complex Roots in Differential Equations

    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.
  10. P

    MHB Solving Coupled ODEs: Analytical Solutions?

    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...
  11. A

    MATLAB How to solve complex 1st order ODEs in octave/Matlab

    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...
  12. C

    Second order system of odes with variable coefficients

    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.
  13. C

    Green's functions for ODEs, jump conditions

    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...
  14. S

    Solving ODEs Using Laplace: Two Challenging Problems

    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...
  15. C

    How Do You Solve a System of Second Order ODEs with Matrix Methods?

    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...
  16. M

    Stability Analysis for Implicit Euler Method with Negative Amplification Factor

    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...
  17. R

    MHB Advanced topic in Odes 2

    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...
  18. R

    MHB Advanced Topic in Odes 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 ' = lambda * y dy / dx = lambda * y dy / y = lambda dx ln y = lambda * x + C y = [ C / lambda ]e^( lambda * x ) This is what...
  19. T

    Found a cool Non-autonomous Coupled System of ODEs

    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...
  20. J

    About Solvable/Unsolvable ODEs

    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 !
  21. MarkFL

    MHB Amber's questions at Yahoo Answers regarding linear first order ODEs

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

    Absolute value in separable ODEs?

    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...
  23. R

    Fortran programming to solve ODEs

    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...
  24. G

    Few questions about series solution of ODEs

    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...
  25. J

    Is the System of ODEs Defined by Matrix B Decoupled?

    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...
  26. J

    Solving Decoupled System of ODEs with Matrix b

    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...
  27. K

    MHB Proving that a system of twelve ODEs satisfies Lipschitz condition

    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...
  28. N

    MHB Recasting/Reducing ODEs of order n to first order

    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...
  29. D

    MHB Coupled ODEs from Euler Lagrange eq

    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] &=...
  30. R

    Upper-level Linear Algebra or upper-level ODEs?

    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...
  31. Astrum

    Coupled ODEs in Electromagnetism

    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...
  32. K

    MHB Solving an IVP for a system of ODEs

    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.
  33. MarkFL

    MHB Jimmy Mai's ODEs Questions at Yahoo Answers

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

    MHB What are the fixed points and stability of a non-linear system of ODEs?

    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...
  35. Z

    MHB Solve Linear System of ODEs | x(0)=x0,y(0)=y0,z(0)=z0

    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...
  36. MarkFL

    MHB Jerome's questions at Yahoo Answers regarding inhomogeneous linear ODEs

    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.
  37. P

    Solving a system of ODEs using Runge-Kutta

    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...
  38. A

    Can Elimination Method Reduce the Order of Differential Equations?

    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...
  39. S

    Checking solution for a system of ODEs

    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...
  40. S

    Setup for a two spring/two mass system (ODEs)

    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...
  41. D

    What is the Three-Body Problem in Physics and Why is it Considered Unsolvable?

    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...
  42. T

    Finding particular solutions of ODEs'

    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...
  43. S

    Wronskian to determine lin.ind. of solutions to a system of ODEs

    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...
  44. Z

    General Solution to Non-homologous ODEs

    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+-...
  45. A

    Linearizing Non-Linear ODEs: How to Transform Equations for Easier Solving?

    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...
  46. H

    Flash vaporization balance - ODEs, deviation variables, linearization

    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...
  47. A

    What are constant coefficients in ODEs?

    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...
  48. M

    Solving an ODE using substitution and integrating factor

    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...
  49. H

    MHB How can nonlinear ODEs be solved effectively?

    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!
  50. H

    MHB Q How to Solve Nonlinear ODEs with Two Variables and Homogeneous Equations?

    I need to solve 2 ODEs: 1. http://www.sosmath.com/CBB/latexrender/pictures/7b213e6c9e4d5fd9d92877694610ac22.png 2. http://www.sosmath.com/CBB/latexrender/pictures/528f96046147932945da54b7a47f97a9.pngbut i can't figure out a way to. Please help!
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