What is Ode: Definition and 1000 Discussions

An ode (from Ancient Greek: ᾠδή, romanized: ōdḗ) is a type of lyrical stanza. It is an elaborately structured poem praising or glorifying an event or individual, describing nature intellectually as well as emotionally. A classic ode is structured in three major parts: the strophe, the antistrophe, and the epode. Different forms such as the homostrophic ode and the irregular ode also enter.
Greek odes were originally poetic pieces performed with musical accompaniment. As time passed on, they gradually became known as personal lyrical compositions whether sung (with or without musical instruments) or merely recited (always with accompaniment). The primary instruments used were the aulos and the lyre (the latter was the most revered instrument to the ancient Greeks).
There are three typical forms of odes: the Pindaric, Horatian, and irregular. Pindaric odes follow the form and style of Pindar. Horatian odes follow conventions of Horace; the odes of Horace deliberately imitated the Greek lyricists such as Alcaeus and Anacreon. Irregular odes use rhyme, but not the three-part form of the Pindaric ode, nor the two- or four-line stanza of the Horatian ode. The ode is a lyric poem. It conveys exalted and inspired emotions. It is a lyric in an elaborate form, expressed in a language that is imaginative, dignified and sincere. Like the lyric, an ode is of Greek origin.

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  1. D

    MHB Solve Repeated Roots ODE: $y' = \begin{pmatrix}1 & 2\\ 0 & 1\end{pmatrix}y$

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  2. D

    MHB Checking some linear ODE solutions

    $y''+y = e^{it}+e^{3it}$ Solution $y = Ae^{it}-\dfrac{1}{8}e^{3it}-\dfrac{it}{2}e^{it}$ and $y''+4y=1+\sin t+\sin 2t$ Solution $y=A\cos 2t + B\sin 2t + \dfrac{1}{4} + \dfrac{1}{3}\sin t - \dfrac{t}{4}\cos 2t$ Correct?
  3. M

    Solution to 2nd order ODE using the D operator method with 2 trig terms on RHS

    Hey, I have the DE y'' -2y' + 3y = xsin(x) + 2cosh(2x) Using the D operator as D = \frac{dy}{dx} this becomes (D2 -2D +3)y = xsin(x) + 2cosh(2x) so yp = \frac{1}{p(D^2)} operating on xsin(x) + 2cosh(2x) (i think) So i know if this was say \frac{1}{p(D^2)} operating on...
  4. U

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    Is there a general solution to \frac{d}{dt}\left[p(t)\frac{dx(t)}{dt}\right] + q(t)x(t) = 0 for x(t) when p(t) and q(t) are arbitrary functions? Better yet, does this question have a name, or some identifier, that I could look in to? It might appear more familiar written as...
  5. K

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  6. S

    Exploring the Power Law Relationship between Mass and Metabolic Rate from ODE

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  7. M

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  8. R

    MATLAB MATLAB - Using solution of one ODE in another

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  9. A

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  10. E

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  11. T

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  12. D

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  13. C

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  14. L

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  15. K

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  16. O

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    second ODE, initial conditions are zeros at infinity! I want to know the temperature profile of phase transition layer in the interstellar medium. For stationary solution, the dimensionless differential equation I ended up with is \frac{d^2T}{dx^2} = \frac{f(T)}{T^2} - \frac{1}{T} where f(T)...
  17. H

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  18. R

    MHB Linear ODE for a fundamental solution set

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  19. B

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  20. M

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  21. S

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  22. A

    How to Integrate a Single ODE in F90 for Water Flow Simulation?

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  23. U

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  24. C

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  25. Runei

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  26. J

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  27. A

    MATLAB Problem with four system ode matlab

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  28. M

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  29. B

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  30. R

    MATLAB How to use Matlab ODE solver events to stop an integration

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  31. E

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  32. F

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  33. F

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  34. C

    MATLAB Solving coupled ode in matlab help

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  35. S

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  36. P

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  37. N

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  38. L

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  39. T

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    Hi everyone, I've got a one-dimensional non-autonomous ODE of the following form: dy / dx = f(x,y;w) x_{0} = g(w) y_{0} = h(x_{0};w) --- i.e., w is a parameter that influences both the derivative dy/dx along with both coordinates in the initial condition (x_{0},y_{0}). I basically want to...
  40. J

    What is the missing term in the differential equation?

    Given the following differential equation: \frac{dy}{dx}=\frac{\sigma y(\alpha x^{\alpha-1}y^{\beta}-\delta-\rho)}{x^\alpha y^\beta-\delta x-y} and starting condition x(0)=x0 (=3, for instance) and these parameters \alpha = 0.2; \beta = 0.1; \rho = 0.014; \delta = 0.05; b = 0.5...
  41. M

    ODE y''+b^2 y=0 where b is vector

    Hi, please help me with this task. I'm wondering what is the right result. I have a ODE y'' - b^2 y =0 also the result should be y=C e^{\pm bx} but what is the result when b is vector? \vec b=(b_x, b_y) is this the result? y=C e^{\pm \vec{b}x} or this? y=C e^{\pm |b| x}...
  42. S

    Separation of Variables for ODE

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  43. Kawakaze

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  44. R

    Struggling with Fourier Transform in Math Methods Class

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  45. O

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  46. P

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  47. M

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  48. E

    Engineering Find impedance of a 2nd ODE circuit (PSPICE)

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  49. J

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  50. M

    How to Solve an ODE Problem when one of parameters is dependent to derivative?

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