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. L

    C/C++ [C++] Using Runge-Kutta order 4 to solve system of ODEs

    (DISCLOSURE: I have already posted this problem in http://math.stackexchange.com/questions/256393/calculate-runge-kutta-order-4s-order-of-error-experimentally, but found no satisfactory answer) The problem is this. I need to experimentally check that RK4 method has an error of order 4...
  2. M

    Help with Octave for system of ODEs

    Hi, I am having a lot of trouble with Octave as I try to solve a system of ODEs. Any help is appreciated, I am a complete newbie with Octave and numerical solving. Let's try a very simple one. Suppose I had a pair of ODEs with a and b being functions of time \frac{da}{dt}=2ba...
  3. STEMucator

    Solving First Order ODEs: Tips & Tricks

    Homework Statement Couple of ODE's I'm having trouble with, a bit rusty. They're all first orders. (1) y' - y = -y3 (2) http://gyazo.com/4a83c6f72c552d1679b9bf95f644599c Homework Equations Substitution, integrating factors. The Attempt at a Solution I'm not quite sure how...
  4. G

    Solving system of 2nd order coupled ODEs

    I have to derive equations of motion from Lagrangian and stumbled upon the following system of equations (constants are simplified, that information is unneeded) \begin{cases} \ddot{x}-A\dot{y}+Bx=0 \\ \ddot{y}+A\dot{x}+Dy=0 \end{cases} This is an extension of a simpler problem where B=D...
  5. D

    Converting a second-order ODE into system of first-order ODEs

    This is not homework, but rather me just trying to work a numerical analysis problem. I have a second order equation on the form m*y'' = a*y + n*x (no first derivative) How does one convert this? It's been years since I did this. Last I remember, one would start with substituting the...
  6. D

    Linear homogenous ODEs with constant coefficients

    Given the ODE of the form: y''(x) + A*y'(x) + B*y(x) = 0 If we choose a solution such that y(x) = e^{mx} and plug it into the original ODE, the ODE becomes: (m^{2} + A*m + B)e^{mx} = 0 If we solve for the roots of the characteristic equation such that m = r_{1}, r_{2} (root 1 and root 2...
  7. T

    Why does reduction of order work for linear ODEs?

    This is not a homework problem, I just want to understand some theory behind this mathematical method. Specifically, if we know that one solution is y1(t), then why is the second solution in the form y2(t) = v(t) * y1(t)? Where v(t) is the function that you need to solve for. Why does...
  8. Z

    Solving Three-Tank System Modeled by ODEs

    Consider a three-tank system modeled by the equations: x_1' = -5x_1+5x_3 x_2' = 5x_1-2x_2 x_3' = 2x_2-5x_3 (A) Initially there are 10 pounds of grain in each tank. What will the amounts be as t \rightarrow \infty? (B) Solve the system and verify your conclusion from (A). I'm...
  9. N

    Particular Solution of 2nd Order ODE: x^2y"-4xy'+6y=ln(x)

    I was wondering what a guess would be for the particular solution of the right hand side of an equation if it looked like this: x^{2}y" - 4xy' + 6y = ln(x) My textbook has some specific examples of the right side function along with the corresponding form of the particular solution...
  10. D

    MHB Converting ODE to a system of ODEs

    Given $x''-x+x^3+\gamma x' = 0$. Is the below correct? Can I do this? The answer is yes. Let $x_1 = x$ and $x_2 = x'$. Then $x_1' = x_2$. \begin{alignat}{3} x_1' & = & x_2\\ x_2' & = & x_1 - x_1^3 + \gamma x_2 \end{alignat} Then I have the above linear system from the given ODE.
  11. D

    MATLAB Using Matlab to plot a phase potrait for ODEs

    First create the function file and name it whatever you would like. I prefer phase-portrait. % Phase Plot Program % To use this function, do the following: % >> phase_portrait(x1, x2, y1, y2, tfinal, 'F', N); for example, % >> phase_portrait(-5, 5, -5, 5, 10, 'F', 5)function [] =...
  12. N

    Coupled set of ODEs and Laplace Transform

    Homework Statement Hi I have a set of five coupled ODE, and I would like to find a solution to the first variable X in the set (the rest I call Y, Z, V, W). The equations are of the form \frac{dX}{dt} = A + BY - CX This isn't homework, but something I been working with for some time. OK, so...
  13. V

    Existence of divergent solutions to system of ODEs

    My question is in regards to systems of ordinary differential equations. One of my research topics right now involves working with some complicated coupled ODEs used to model ecological stuff. Without getting into the details, the model I am working on now has a bad tendency to diverge for...
  14. I

    Does anyone know a resource for advanced Methods for ODEs, Integrals, etc.

    Is there a resource that is just a walkthrough of various kinds of problems one might get and the ways to solve them? I'm not talking about the basics from the calc and difEQ series (u substitution, partial fraction decomposition, trig substitutions, trig power reduction, integration by parts...
  15. D

    MHB Find the eigenvectors problem help

    Just checking a solution. $y' = \begin{pmatrix}4 & -1\\ 2 & 1\end{pmatrix}y $ $$ \lambda^2 - 5\lambda + 6 = (\lambda - 3)(\lambda - 2) = 0. $$ So the eigenvalues are $\lambda_1 = 3$ and $\lambda_2 = 2$. To find the eigenvectors, we must solve $(4 - \lambda)y_1 - y_2 = 0\iff y_2 = (4 -...
  16. B

    Analytical method to solve a system of ODEs

    Hello All, I am new to this community but by reviwwing the questions and answers posted in this forum I was encouraged to share my question with you and I hope you can help me. I have a system of 4th order ordinary differential equations for several functions which I call them: y_1,y_2...
  17. S

    Superimposition principle in solving ODEs

    Hi all, first of all, I have to admit I have often used this richness of knowledge that permeates through the posts of this forum to find answers to questions that I have come across in my studies. Thanks for all! Now, I have a question to post, for the first time. I am trying to teach...
  18. B

    Solving a system of two nonlinear second order ODEs (Mechanical vibrations)

    I was wondering what the common methods for solving such a system are: 2 m \ddot{x} - m l \ddot{θ} θ + k x = 0 m l^{2} \ddot{θ} - m l \ddot{x} θ + m g l θ = 0
  19. A

    Find all bifurcation points (ODEs)

    I'm at a loss on this question...my troubles seem to be algebraic or that I'm simply missing something.x' = \mu - x2 +4x4 my method for these questions has basically been to do everything required to draw bifurcation diagram bar drawing the actual diagram itself (ie, find equilibria, what...
  20. E

    My issue with using eigenfunction expansion for ODEs

    I have previously taken PDE's and ODE's. I understand obtaining the equation y''+lambda*y=0 (lambda then giving the eigenvalues). But I've encountered now the use of eigenfunction expansion for an ODE; and what I don't understand, is that in solving it they're making some assumption that y''+y=0...
  21. A

    Semi-implicit method for ODEs?

    I have two coupled ordinary differential equations: \displaystyle \frac{dx}{dt} = f(y) x \displaystyle \frac{dy}{dt} = s(x) y To solve these equations, we generally use explicit method, but these equations are stiff equations. Therefore semi-implicit method might be a better choice. I'm...
  22. T

    Transforming a system of PDEs into a first order system of ODEs

    Homework Statement Say we have a system of N PDEs, each with even order. That is, say the k^{th} equation has order 2 m_k. If m_i = m_j for all i and j, then we can transform the system of PDEs into a first order system of ODEs by introducing new variables. However, if m_i \neq m_j for some...
  23. T

    How Do You Solve for Non-Zero Steady States in a Tri-Variable ODE System?

    I'm running into a problem. This is mainly for reading over the summer and I'm working on getting through a dynamical systems book on my own. I've come across a system that I'm not too sure on the procedure. Consider the following system of differential equations: \frac{dX}{dt} = 1 - X -...
  24. A

    Re-write as a system of first order ODEs

    hello, I am going through the first chapter (a review chapter) of a second-course book in ODEs, and can't seem to remember how to re-write higher order DEs into a system of first order linear ODEs, and my old textbook only shows this for second order equations... The question is: "Write the...
  25. T

    Question about 2nd order linear ODEs series solutions

    I got some questions about this topic... y'' + p(z)y' + q(z)y=0 where y (and its derivatives) is a function of z, z ∈ ℂ. 1) My books says this: In points where both p(z) and q(z) are analytic, y(z) is also analytic. But in points where p(z) or q(z) (or both) aren't analytic, y(z) may not...
  26. J

    Solving ODEs: Is There Any Hope?

    Hello Comming from Discrete Mathematics, I have very little knowledge in Solving ODEs: I have the following equation (where E(x) is an ordinary generating function). E'(x) = \frac{(E(x)*E(x) +E(x)-x)}{2x*E(x)} with E(0) = 0 Is there any hope to solve this equation?
  27. L

    Unsolvable Linear First-Order ODEs with Boundary Conditions

    Homework Statement Out of a set of differential equations with boundary conditions, there are three (first order) equations I couldn't solve. These are: Homework Equations 1. \frac {dy} {dx} = \sqrt{x + y}, y(1) = 0. 2. \frac {dy} {dx} = 2y(x \sqrt{y} - 1), y(0) = 1. 3. 2x^2...
  28. K

    Inverse Transformations of ODEs

    Homework Statement F(s) = s/((s-1)(s^2+1)) F(s) = (s/(s^2+4s+5))(e^(-3s)) Homework Equations Don't believe there are any. The Attempt at a Solution Not particularly sure. I can solve ((s-2)(e^-s))/(s^2-4s+3), but seem to be having problems with these.
  29. O

    MHB Homogeneous linear ODEs with Constant Coefficients

    do you have a idea about it?can you help me http://img17.imageshack.us/img17/1156/18176658.png
  30. K

    Programs Does a pure math major need to take ODEs?

    Right now I'm a sophomore at a state uni with hopes of getting into graduate school in pure mathematics. When I was a freshman, I surveyed the three major areas of math - analysis, algebra, and topology - and I decided that analysis was for me. Although I did very well in Algebra, I found it...
  31. P

    MATLAB MATLAB solution to system of ODEs with forward and backward propagation

    I have a system of coupled ODEs which tells the propagation of power Pi in an optic fiber. \frac{\partial P_i }{\partial z} = \left (N\sigma - 1 \right ) P_i where N = \frac{\sum_i \alpha_i P_i}{\sum_i \beta_i P_i + 1} If the signals are copropagating, there is no problem since...
  32. T

    Writing a system of 2 ODEs as a 1st order ODE

    Homework Statement Consider the following initial value problem for two functions y(x),z(x): 0 = y''+(y'+7y)\text{arctan}(z) 5z' = x^2+y^2+z^2 where 0 \leqslant x \leqslant 2,\; y(0)=1.8,\;y'(0)=-2.6,\;z(0)=0.7. Rewrite the system of ODEs in standard form using a suitable substitution...
  33. S

    Numerical evaluation of systems of ODEs

    I'm looking to do numerical evaluation of a system of differential equations and would like to use the RK4 method however I'm having a problem as my differential equations are respect to different variables and I don't know how to adapt RK4 to allow for that. The general form of the equations of...
  34. A

    Finding an Integrating Factor for a Diffential Equation

    Integrating Factors for ODEs (Question from Boas) Find an integrating factor by inspection to make the below differential equation exact. (y^2-xy)dx+(x^2+xy)dy=0 I've been inspecting, but I'm not seeing it! Is there a way to analyze this in my head that will lead me more easily to the...
  35. A

    Learning Math Differently: Understanding ODEs

    Hi, Usually, it takes a while for me to digest information, because I have a lot of filters in my mind and to remember and understand things I have to put all the new information in context. I have to have an interpretation of the content. For this reasons I am doing terribly in my ODE course...
  36. S

    Where does the general solution for second order linear ODEs come from?

    If ay+b\int^y_0ydy+cy'=0 then ay'+by+cy''=0 now, let y=e^{sx} thus, s^2+a/cs+b/c=0 and then one solves for s. It is then plugged into what sources are deeming a "general solution" y=C_1e^{s_1x}+C_2e^{s_2x} however, none of these texbooks explain or derive where this comes from, and I have not...
  37. A

    How can I reduce the order of these troublesome ODE systems?

    Hi everybody, I've troubles with the following two systems of differential equations: image hosting gif I tried to reduce the order but I wasn't able to do anything...
  38. T

    Is this a legitimate method for solving first order ODEs in fractional form?

    Suppose we have some ODE given by y' = G(x,y)/H(x,y). Let x and y depend on a third variable, t, so that x and y are parametrized in a way. Then applying the chain rule to y' gives \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{G(x,y)}{H(x,y)} Then comparing the numerators and...
  39. P

    Laplace Transform of Systems of ODEs with variable coefficients

    Homework Statement Say you have: EQ1: y1''*t+y1'*t+y2=0 and EQ2: y2''*t+y2'*t+y1=0 y1(0)=0,y1'(0)=0,y2(0)=0,y2'(0)=0 Homework Equations The Attempt at a Solution I can get it so far, but having both y1 and y2 really gives me fits: Eq1: Y1(-2s-1)+dY1/ds(-s2-s)=-Y2...
  40. T

    Analytically solving ODEs with non-constant coefficients for a specific t

    Given an ODE in the form of f(t)y''+g(t)y'+h(t)y=0 If all I am looking for is the y(t) at a specific value of t and NOT the general solution, can I just plug in that value of t into the original ODE and then solve it analytically or is a numeric solution the only way?
  41. G

    Exploring Parametric Changes in ODEs: Analytic Way

    The defining equations are: dx/dt = -(y + z) dy/dt = x + ay dz/dt = b + z(x - c) where a = b = 0.2 and 2.6 ≤ c ≤ 4.2. Is there an analytic way of showing that by changing the parameter c, we can get period-1 orbit, period-2 orbit, period-4 oribt, period-8 orbit, etc. and for c > 4.2...
  42. J

    Using eigenvalues and eigenvectors to solve system of ODEs

    Homework Statement Use eigenvalues and eigenvectors to find the general solution of the system of ODEs.. x1 = 3x1 - x2 x2 = -x1 + 2x2 - x3 x3 = -x2 + 3x3 Homework Equations The Attempt at a Solution I converted that into the matrix...
  43. S

    Solving ODEs: y=xp+f(p): Show General Solution & Second Solution

    I've been asked to consider differential equations of the form y=xp+f(p), where p=dy/dx, and to show that the general solution is y=cx+f(c). Substituting in p, the original equation is y=x(dy/dx)+f(dy/dx), and by differentiating I get: dy/dx=x(d2y/dx2) + dy/dx + d2y/fx2 * f`(dy/dx)...
  44. L

    Solving 2nd-Order ODEs: y'' + 2y' + y = f(t); y0=y0'=0

    Homework Statement y'' + 2y' + y = f(t); y0=y0'=0 f(t) is piecewise -- 1 for 0 < t < a; 0 for t > a Use y(t) = ∫G(t,t') f(t') dt' with bounds 0 to infinity 2. The attempt at a solution I don't really have any logical attempt. My highest math is diffy q 1, Calc 3 and LA 1, I...
  45. J

    Mathematica Troubleshooting NDSolve Errors: Non-Numerical Values in ODE Integration

    I'm having a problem with NDSolve. See attached picture. I have a package generating a set of ODE's, which I display, and then the next line is the NDSolve integration. I get an "Encountered non-numerical value for a derivative at t==0" error, and I can't spot the mistake. The one thing that...
  46. R

    What are the ODEs for a vehicle in motion under gravitational pull?

    I'm attempting to find a system of ODEs for a vehicle in motion that undergoes acceleration due to the gravitational pull of different bodies in space. It has an initial velocity, but doesn't undergo any change in acceleration due to thrust. This vector represents its motion...
  47. V

    Solving 3 Coupled ODEs with a Constraint

    while solving Lagrangian of a system to derive equations of motion in presence of a constraint, I have finally landed down to a system of 3 coupled ODEs , where i have two variables(x and y) and 1 Lagrange multiplier. ODEs are of order 4,3 and 1 respectively. L1(x,y)=lambda L2(x,y)=0...
  48. F

    [ODEs] Exact Equations and Substitution

    Okay, I'm going insane. I have these problems completely worked out and have stared at them for centuries but the online homework is still telling me they're wrong. Could anyone here take a look and let me know? I'd appreciate it a ton. Problem 1: Exact Equation Homework Statement...
  49. M

    ODEs: Word problem involving (I think) phase lines

    Homework Statement If the population y of rats on a farm at time t (in weeks) satisfies: dy/dt = -y(y-100)/50 then how many rats per week should be killed to eradicate the population? Homework Equations None known. The Attempt at a Solution The ODE dy/dt is autonomous, so I can...
  50. M

    Verifying Differential Equations Solutions: ODEs on Intervals

    Hi! I think I have to ask this since I'm having health problems- from Kreyszig, for xy'=-y how do you verify the solution y=h(x)=clnx by differentiating y'=h'(x)=-clnx^2? I don't see how you get the x^2 term also for ODEs the solution is on an open interval a<x<b but how does it include...
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