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. I Fundamental matrix of a second order 2x2 system of ODEs

Let ## \mathbf{x''} = A\mathbf{x} ## be a homogenous second order system of linear differential equations where ## A = \begin{bmatrix} a & b\\ c & d \end{bmatrix} ## and ## \mathbf{x} = \begin{bmatrix} x(t)\\ y(t)) \end{bmatrix} ## Now to solve this equation we transform it into a 4x4...

46. Solving Higher Order ODEs: y''''''+y'''=t

Homework Statement y''''''+y'''=t Homework EquationsThe Attempt at a Solution I got all the roots and solved the homo eq. Then I tried to guess the partial eq and got At+B However, I don't know how to proceed because the 6th derivative or the 3rd would be 0.
47. C++ Alternatives to Euler's Method for Solving ODEs

Hi, Apart from the Euler's method, is there any other method (with better efficiency) that can let us solve an Ordinary Differential Equation of the form \frac{dy}{dx}= f(x,y)?
48. Solving Separable ODEs: How to Integrate with Functions of t?

I understand how to integrate this: ∫y2dy. I don't understand how to integrate this: di(t)/dt = i(t)p(t) intergrate((di(t)/dt/i(t))*dt = p(t)dt) (see this image: http://i.imgur.com/OdKI309.png) how do you perform the intergral on the left, seeing as as it not dt, but di(t)? thanks
49. Dealing with boundary conditions in system of ODEs

Homework Statement I'm trying to plot the steady state concentration of yA vs. x, yB vs x and yu vs x using centered finite difference method. Homework Equations The Attempt at a Solution τ represents the dimensionless time variable, so steady state would mean that the left hand side of...
50. Finite difference discretization for systems of higher ODEs

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