What is Ode system: Definition and 29 Discussions

"Ode: Intimations of Immortality from Recollections of Early Childhood" (also known as "Ode", "Immortality Ode" or "Great Ode") is a poem by William Wordsworth, completed in 1804 and published in Poems, in Two Volumes (1807). The poem was completed in two parts, with the first four stanzas written among a series of poems composed in 1802 about childhood. The first part of the poem was completed on 27 March 1802 and a copy was provided to Wordsworth's friend and fellow poet, Samuel Taylor Coleridge, who responded with his own poem, "Dejection: An Ode", in April. The fourth stanza of the ode ends with a question, and Wordsworth was finally able to answer it with seven additional stanzas completed in early 1804. It was first printed as "Ode" in 1807, and it was not until 1815 that it was edited and reworked to the version that is currently known, "Ode: Intimations of Immortality".
The poem is an irregular Pindaric ode in 11 stanzas that combines aspects of Coleridge's Conversation poems, the religious sentiments of the Bible and the works of Saint Augustine, and aspects of the elegiac and apocalyptic traditions. It is split into three movements: the first four stanzas discuss death, and the loss of youth and innocence; the second four stanzas describes how age causes man to lose sight of the divine, and the final three stanzas express hope that the memory of the divine allow us to sympathise with our fellow man. The poem relies on the concept of pre-existence, the idea that the soul existed before the body, to connect children with the ability to witness the divine within nature. As children mature, they become more worldly and lose this divine vision, and the ode reveals Wordsworth's understanding of psychological development that is also found in his poems The Prelude and Tintern Abbey. Wordsworth's praise of the child as the "best philosopher" was criticised by Coleridge and became the source of later critical discussion.
Modern critics sometimes have referred to Wordsworth's poem as the "Great Ode" and ranked it among his best poems, but this wasn't always the case. Contemporary reviews of the poem were mixed, with many reviewers attacking the work or, like Lord Byron, dismissing the work without analysis. The critics felt that Wordsworth's subject matter was too "low" and some felt that the emphasis on childhood was misplaced. Among the Romantic poets, most praised various aspects of the poem however. By the Victorian period, most reviews of the ode were positive with only John Ruskin taking a strong negative stance against the poem. The poem continued to be well received into the 20th century, with few exceptions. The majority ranked it as one of Wordsworth's greatest poems.

View More On Wikipedia.org
  1. Alwar

    I How to Find the Generalized Eigenvector in a Matrix ODE?

    Hi, I have a set of ODE's represented in matrix format as shown in the attached file. The matrix A has algebraic multiplicity equal to 3 and geometric multiplicity 2. I am trying to find the generalized eigenvector by algorithm (A-λI)w=v, where w is the generalized eigenvector and v is the...
  2. V

    Adding noise and solving stochastic ODEs in Python

    The Coupled ODE Model Below are my coupled differential equations, where the only variable I try to meddle with is the ITMblood. The motivation here is if I try to increase ITMblood (in the next section I will show how I do it), at some concentration of ITMblood (most likely a very huge one) ...
  3. Dwightun

    Maple How to get my function from these dsolve results

    Hi! I'm trying to solve ODE system with 2 equations Here is a result from dsolve. How can i get R(t) out of it And how to substitute initial conditions in it?
  4. M

    A How can the stability of an ODE system be determined without solving it?

    Hi PF! Given the ODE system ##x'(t) = A(t) x(t)## where ##x## is a vector and ##A## a square matrix periodic, so that ##A(t) = A(T+t)##, would the following be a good way to solve the system's stability: fix ##t^*##. Then $$ \int \frac{1}{x} \, dx = \int A(t^*) \, dt \implies\\ x(t) =...
  5. N

    Partial Differential Equation with variable coefficients

    Homework Statement This question relates to a very large project I have been assigned in a course on mathematical methods in structural engineering. I have to solve the following equation, in a specific way: (17) Now we have to assume the following solution: (18) It wants me insert...
  6. Theia

    MHB Looking for a serie solution for a nonlinear ODE system

    Hi! \begin{cases} \dot{q} = a \left( 1 - q^2 \right) \\ \dot{a} = - \alpha - a^2 q\end{cases} \qquad \alpha \in (0, 1 ) I've looked into this ODE system about 7 months now, but I've not got anything promising how to write down the solution. I'm mostly interested in q-serie. (To those of you...
  7. incredibe1999

    Maple ODE System Solution Maple: Plotting Earth's Orbit with Sun at Origin

    Hey there! I was trying to plot a ODE solution, but am not getting what I should be. It is actually plotting the orbit of Earth with Sun at the origin. My equations The (-0.00011847) is GM. The Initial Conditions: The plot I get: Should not I be getting a elliptic/circular plot as the...
  8. S

    A Numerically calculating the solution for a non-homogeneous ODE system

    I have been solving system of homogeneous ODE numerically using Crank-nicolson (CN) method but now I have a system of non-homogeneous ODE. It would seem that CN would not work since the rank of the matrix will be less than the dimension of the matrix. Is there any other method that can...
  9. N

    Find the approximate linear ODE system

    dx/dt = x-y^2 dy/dt= x^2 -xy -2x For each critical point, find the approximate linear OD system that is valid in a small neighborhood of it. I found the critical points which are (0,0),(4,2),(4,-2) but have no idea how to do the above question! please help!
  10. B

    Estimating the Parameter 'a' from ODE System

    Hi everyone I have a system of ODE as follows x1_dot=f1(t)-ax1 x2_dot=f2(t)-ax2 x3_dot=f3(t)-ax3 f1,2,3(t) are unknown nonlinear functions of time, a is constant and unknown, x1,2,3 and their derivatives are given. How can I estimate the parameter a from the given information? Thanks
  11. A

    Trapping region for a nonlinear ODE system

    I need to find a trapping region for the next nonlinear ODE system $u'=-u+v*u^2$ $v'=b-v*u^2$ for $b>0$. What theory i need to use or which code in Mathematica o Matlab could help me to find the optimal trapping region.
  12. S

    Forward Euler Method for ODE system

    Homework Statement Solve the following system for 0<t<5 u^\prime = u-e^{-2t} v, u(0) = 1 v^\prime = u+3v, v(0) = -2 using Forward Euler method and implement the numerical scheme into a MATLAB code. Homework Equations Forward Euler : \vec x^(\prime)_{n+1} = \vec F(t,\vec x)...
  13. W

    Change ODE system to Polar to apply Poincare-Bendixson

    Question: Show that the system x'= x-y-x[x^2 + (3/2)y^2] y'= x+y -y[x^2 + (1/2)y^2] has at least one periodic orbit. I know that I need to apply Poincare-Bendixson Theorem. I can prove the first three points of it easily, but to create a trapping region, I believe that I need to...
  14. K

    Homogeneous ODE system, how to solve using WOLFRAM

    Hi. If I have a homogeneous ODE with constant coefficient system in the form of 2x2 matrix: X'=A X, A is a 2x2 matrix. How do I solve this using wolfram or matlab?
  15. J

    MHB ODE system. Limit cycle; Hopf bifurcation.

    Problem: The following two-dimensional system of ODEs possesses a limit-cycle solution for certain values of the parameter$a$. What is the nature of the Hopf bifurcation that occurs at the critical value of $a$ and state what the critical value is. $\dot{x}=-y+x(a+x^2+(3/2)y^2)$...
  16. S

    ODE system. Limit cycle; Hopf bifurcation.

    Homework Statement The following two-dimensional system of ODEs possesses a limit-cycle solution for certain values of the parameter a. What is the nature of the Hopf bifurcation that occurs at the critical value of a and state what the critical value is. Homework Equations...
  17. J

    MHB ODE system, plane-polar coordinates

    I have: $\dot{x}=4x+y-x(x^2+y^2)$ $\dot{y}=4y-x-y(x^2+y^2)$ And I need to find $\dot{r}$ and $\dot{\theta}$ I got as far as: $\dot{x}=r(\text{sin}(\theta)-\text{cos}(\theta)(r^2-4))$ $\dot{y}=r(-\text{sin}(\theta)(r^2-4)-\text{cos}(\theta))$ How do I go from here to $\dot{r}$ and...
  18. C

    MATLAB Non linear ODE system matlab fourier analysis problem

    Hello all. I am studying a system and want to investigate how the frequency of y(3) varies under different conditions. However, my the fft I perform on it tells me the frequency is zero, which must be incorrect. I have tried a stack of things but can't see what the problem is. I'm relatively...
  19. Y

    ODE System with Variable Coefficients

    hi suppose we have this equation : d/dt(X)=A(t)*X x is a n by 1 column matrix and A is a n by n matrix that is the matrix of coefficients. coefficients of equations and consequently A are depend on t which is time. how i Solve this equation ? thanks
  20. M

    Solving a First Order Linear ODE System with a Constraint

    Hello all, I don't have much experience with ODEs. I have a simple system, which I believe is first order linear, similar to the following: dA/dt = 2A + 3B - C dB/dt = A + 2B - C dC/dt = -2A + 5B - 2C Now I would like to include the constraint that A + B + C = 1. How do I do this...
  21. M

    Reducing Second Order ODE system to First Order

    Homework Statement A 3-storey building can be modeled as a system of coupled masses and springs as showen in attached document. Where mi is the mass of each floor, ki is the spring constant, xi is the displacement of each floor, and ci is the damping coeffcient.Homework Equations I understand...
  22. U

    MATLAB Troubleshooting ODE Systems in MATLAB: Common Errors and Solutions

    Hi to everyone, I have some problem in implementing a ODE system in matlab. function dC = Model(x,C) dC = zeros(2,1); dC(1) = -2/C(1) -3*dC(2); dC(2) = -3/C(2) -4*dC(1); [x,C] = ode23(@Model(x,C),[0 300],[56.9 0]); plot(x,C) The debugger says "? Input...
  23. Z

    Nonlinear ODE System: Computing w' & Finding R

    Given the ODE system: v' = u(u2-1) u' = v-u Define w=u2+v2. Compute w'. Find the largest radius R for which u2+v2<R so that the if the solution curve (u,v) is inside that circle the solution tends to (0,0) as t--> +\infty Any guidance would be appriciated !
  24. S

    Solving Tricky ODE System Homework

    Homework Statement I have 3 masses in 1-D connected by two springs. A driving force is exerted on the first mass and i need to derive the equation of motion of the last mass. I have worked out the Lagrangian to determine the equations of motion but cannot solve for z. Homework Equations The...
  25. C

    Help ODE System Stability - Origin Analysis

    Homework Statement Hello. I want to study the stability of the origin of the following problem: dx/dt = -2y dy/dt = x + 2y dz/dt = -2z So the eigenvalues of this 3 x 3 matrix are -2, 1 + i, 1-i. The eigenvectors are (0,0,1) , (2,-1-i,0), (-2,-1+i,0)...
  26. G

    Complex ODE system numerically - GSL ODE SOLVER

    Hi, I need to solve very large complex ODE system. It is about time evaluation of system, which is at time t=0 in eigenstate with the smallest eigenvalue. For my test case I am trying to solve smaller similar problem, the ODE system is like: C^{'}_{m} = - i \sum^{N-1}_{n=0} C_{n}(t) Exp[...
  27. M

    Transforming Order of ODE System

    Hi i got a question trying to solve some problems from my schools webpage and encountered a problem where I am given 2 RLC-Circuits and the corresponding dgls for the oscillation ( no problem so for all the standart basic E/M stuff) But then I am asked to transform this system of 2 dgl´s of...
  28. M

    Numerical Solution to ODE System - IVP or BVP?

    I have a system of spatial ODEs to solve... Actually a DAE system, but here's the issue: The equations are vaild over a specific domain, x = 0..L The equations are only bound at one point (thier "initial point") but at either 0 or L f1(0)=0 f2(0)=100 f3(L)=0 f4(L)=100 (also an...
  29. Clausius2

    Solving Heavy ODE System to Compute Round Jet Near Field

    In order to solve the near field description of a round jet, I want to work out the variables F(\eta) , \rho(\eta) and Y(\eta) which represents the self similar stream function, density, and mass fraction respectively. The system obtained is...