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.
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...
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...
Hi All
I am rusty with my my math and got stumped with a straight forward question regarding vibrations and complex roots.
I have a 2nd order ODE
x'' +4 x' + 16 x = some forcing funciton
This turns out complex roots. I go through the run around of solving this and I get a...
I'm trying to find a power law relationship between mass and metabolic rate, given that each of these quantities is defined by a differential equation.
Assuming dM/dt=a*M(t) and dR/dt=b*R(t), where M(t) is mass and R(t) is metabolic rate, I know that I can solve each of these equations to...
A car of mass 1200 kg is started from rest and pulled on the level ground by an engine. The resistance of the motion is Kv, where v(m/s) is the velocity of the car at time t(s). The power of the engine is constant and equal to 80000 watts.
a) How does P, the power of the engine connect to F...
Hi all,
I'm trying to use MATLAB to obtain simulations for some equations that describe a model. I'm new to MATLAB (though I've taken a course in C++ and another in Java), so I read a bit on the mathworks website on solving ODEs, and settled on ode45
The equations I'm trying to model are the...
Hi everyone,
I have a problem understanding an ODE and using it to find something particular. Consider the following :
ODE : dC/dt= S-r*C
where
S: synthesis rate
r : death rate
C: population
Co: initial population
the analystical solution is simply C(t) =S/r -(S/r-Co)*exp(-r*t)...
Homework Statement
I'm reading a chapter out of Elem. DE 6th Edition by Rainville and Bedient (Ch 4 pg 61) titled integrating factors found by inspection. To explain it, the authors start with an equation, which is grouped to become:
y dx + x dy + x^3y^2 dy = 0
which then becomes...
I am trying to solve four coupled equations. Three of them are first order differential equations and the fourth is a algebraic one. The equations look something like this:
V_{l}(r) = f_{1}(r)W'_{l}(r) (1)
h''_{l} + f_{2}(r)h'_{l} + f_{3}(r)h_{l}(r) = U_{l}(r) (2)
f_{4}(r)U'_{l} +...
I am not too familiar with differential equations but am familiar with basic calculus, I came across this equation trying to describe a particular function:
dy/dx =((sqrt((y-x)^2+y^2)-abs(y))/(y-x))*abs(y)/y
Anyway I tried to separate the variables unsuccessfully and using v(x)=y(x)/x with...
Homework Statement
Find negative eigenvalues and corresponding eigenfunctions to the following operator:
H:= - \frac{d^2}{dx^2} - \delta_{-r} -2\delta{r} .
(The eigenfunction should be twice contiously differentiable, except for possible jump discontinuities at +-r of the first and...
Homework Statement
Find the Taylor expansion y(x) satisfying: y'(x) = 1 - xy
Homework Equations
The Attempt at a Solution
So I need expressions for y''(x), y'''(x), ...etc
I can find y''(x)=-y-xy' by differentiating implicitly.
By setting y'(x)=z, then dz/dx =...
hi all,
I've been trying to work this problem out,
\frac{dv}{dt}-A(B-v)^{1.6}=G
A, B and G are constants
and Matlab can't give me a solution either. I'm wondering if there is even a solution?
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)...
Hello,
I'm having hard times with the following simple linear ODE coming from a control problem:
$$u(t)' \leq \alpha(t) - u(t)\,,\quad u(0) = u_0 > 0$$
with a given smooth α(t) satisfying
$$0 \leq \alpha(t) \leq u(t) \quad\mbox{for all } t\geq 0.$$
My intuition is that $$\lim_{t\to\infty}...
Question:
For the interval x > 0 and the function set S = { 3ln(x), ln2, ln(x), ln(5x)}, construct a linear ODE of the lowest order.
My work:
Taking the wronskian for this solution set, I get it as 0. Doesn't that mean that a linear ODE for this set cannot be found?
I'm very confused here...
currently i am a math major, still unsure whether pure or applied. i am also looking to double major in physics. which class would be more helpful to me: abstract algebra, or (upper division) ODE class? I have taken the lower division DE class already.
A problem from a heat transfer book with conduction and radiation led me to a differential equation like this:
T'(t) = a - b*T(t) - c*T(t)^4
Although my professor said that there wouldn't be an analytical solution for this one and to get the answer by an iterative method I got curious and...
Homework Statement
We have the autonomous ODE:
\dot{x} = f(x), x \in \mathbb{R}
first we define the following sets:
E := \{f(x) = 0\}
E^+ := \{f(x) > 0\}
f(x) is continuous so E is a closed set and E^+ is an open set.
x_0 \in (x_-,x_+) where (x_-,x_+) is the connected component of E^+...
Hi all,
I've written a simulation of water flow in two dimensions in F90 but I'm having some trouble with it. Water flows from one cell to another using an equation for rate of change of depth and an algorithm for assigning flow direction.
The flow direction bit is fine but the dD/dt...
Hello!
On Pauls notes webpage, there is the following problem to be solved by variation of parameters:
ty''-(t+1)y'+y=t^2 (1)
On the page, the fundamental set of solutions if formed on the basis of the complementary solution. The set is:
y_{1}(t)=e^t and y_{2}(t)=t+1
Now, I must be...
I got trouble in dealing with this kind of system. For example,
Ay``+By`+Cy=0
where y=transpose(y1 y2)
A=(1 0
0 1)
B=(0 1
1 0)
C=(1 1
1 1)
May someone give me a book name?:smile:
2nd Order Homogenous ODE (Two solutions??)
Alright.
I understand that if we have a differential equation of the form
A\cdot\frac{d^{2}y}{dt}+B\cdot\frac{dy}{dt}+C\cdot y = 0
and it has the solution y1(t), and y2 is also a solution. Then any combination of the two
yH=C1y1(t)+C2y2(t)...
They give a differential equation: x' = f_a(x) = ax(1-x) . In determining if the equilibrium points are sources or sinks, they say: We may also determine this information analytically. We have f'_a(x) = a - 2ax
How can they differentiate with respect to x? x is a function, it doesn't...
Hi,
I am a newbie to matlab
I have 4 equations ode to a system,
dxdt=-c*z*s')
dydt=((-1.021*(y^2))/(b+a))-(2.081015257+(6.936717523*x))/(b+a)+((p*r)-(p*j)/(b+a))-(((p^2)-2*p*(s^2)*c*z^2))/2*p')...
I feel very comfortable doing this because I've taken numerical analysis and written a short term paper on numerical approximations for PDEs. I am very strong in linear algebra and have calc I/II.
The reason I ask for advice is because I have just graduated from undergrad with a degree in...
I have a pesky problem, I have this function of time, S(t) and I'm trying to find how far to evaluate S (its an expensive process and must be done for finite t=time). Essentially, I want to measure S until dS/dt ≈ 0. But my current criteria is making the computation itself inefficient not to...
How to use Matlab ODE solver "events" to stop an integration
I'm using Matlab's ODE solver (specifically ode15s) to solve a system of equations. The sum of the values of the equations eventually arrive at a steady state, but the time at which that occurs is dependent on several things, not...
Homework Statement
I have not had luck in finding a solution that describes an object falling. Forces include gravitational force which is constant and a vicous force directly proportional to the cube of the velocity. I am supposed to find v as a function of time.Homework Equations
v' +...
Hi, I'm not sure if this is on the right thread but here goes. It's a perturbation type problem.
Consider the boundry value problem
$$\epsilon y'' + y' + y = 0$$
Show that if $$\epsilon = 0$$ the first order constant coefficient equation has
the solution
$$y_{outer} (x) = e^{1-x} $$...
Hi, I'm not sure if this is on the right thread but here goes. It's a perturbation type problem.
Consider the boundry value problem
$$\epsilon y'' + y' + y = 0$$
Show that if $$\epsilon = 0$$ the first order constant coefficient equation has
the solution
$$y_{outer} (x) = e^{1-x} $$
I have...
Problem: Model the coupled ode system for a motor:
Equations:
dVc/dt=(-1/C)*Il+(1/C)Is
dIl/dt=(1/L)*Vc-(R/L)*Il
I have been given the values of L=1e-3, R=50, Is=10.0A and C is to be designed by trial and error.
I have been able to write out the function, by assigning Vc=x(1) and Il=x(2)...
so I understand the basic premise of differentiating a first ODE, or I thought I did. I have the equation y'-y=abs(x-1). I have no idea of how to go about this. Can someone walk me through how to do this? I'm attempting to study for a test and this is one of the practice questions he gave us so...
hey,
i have this 4th order ode question that I've been working on,
the homogeneous solution was easy enough by finding the particular solution has become a bit annoying,
the ode is
y'''' - 4y'' = 5x2 - e2x
I have gotten the particular solution using variation of parameters...
Hi
I am trying to integrate Newtons equations for my system
a = \frac{F}{m} = \frac{d^2x}{dt^2}
This is only for the first coordinate of the particle. I wish to do it for y and z as well, but let us just work with x for now to make it simple.
The force in the x-direction depends on...
hey,
i'm having trouble with this question,
x y' - y = x2cosx
the solution is
y= xc + xsinx
and we are asked to solve the equation in the following two cases,
1, y(0)=0
and 2, y(0) = 1
but applying these conditions to the general solution gives no information,
in...
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...
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...
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}...
Homework Statement
Solve the following equation by separation of the variables:
y' tan-1x - y (1+x2)-1 = 0
Homework Equations
The Attempt at a Solution
I am not sure if tan-1x stands for arctan x or (tan x)-1. (This has been taken out a book.) Any help on this would be...
Homework Statement
The problem regards a ball thrown vertically, there is a model of the motion that we worked out, from the original equation
a(t) = -(g/b^2)(v^2+b^2)
With some help from another forum member I integrated with regard to t (dv/dt?) this to...
I haven't had differential equations yet, so I am struggling in your math methods class. I understand what a Fourier Transform is, but I'm having trouble with this particular problem.
Homework Statement
Here's a screenshot. Better than I can write it.
http://i.imgur.com/PQ6tB.png
The...
Homework Statement
Solve y^2*(1-(dy/dx)^2)=1
Homework Equations
The Attempt at a Solution
I expressed the ODE in terms of dy/dx and considered two cases. I got
(a) y^2 = 1 + (x+C)^2
(b) y^2 = 1 + (-x+C)^2 where C is a constant
However, my professor told me that there is...
Homework Statement
Solve:
y'' - λy = 0
where y(0)=y(1)=0, y=y(t)
Homework Equations
The Attempt at a Solution
Hi everyone,
This is part of a PDE question, I just need to solve this particular ODE. I know how to do it in the case for y'' + λy = 0, where you get the...
Homework Statement
I've got
y'' - ω2y = sin(ωx) + sinh(ωx) where y(a) = A, y(b) = B
Homework Equations
The Attempt at a Solution
Yc = C1 Sinh(ωx) + C2 Cosh(ωx)
and I got my Yp to be -1/2*sin(ωx) + 1/2*sinh(ωx)
I'm not sure about getting the Y general. Any pointers...
See the circuit diagram attached.
The voltage source is a sinusoidal AC source with amplitude = 240, Frequency = 50, Phase = 90.
Essentially I have a lab report and I was wondering what sort of equations are required to find the impedance of the circuit. We're not really told if we're...
Hey,
We haven't properly covered this in class yet, but I am trying to study ahead using online course notes, I manage to finish a few questions but I have gotten stuck here,
The question starts by asking for the solution to the ODE:
y' = 1 - 2xy,
When I solve this using the...
Hello Guys!
I have an ODE problem that I'm solving it by MATLAB ODE solvers!
in fact I have a system of non-linear differential equations in one of these equations I have a parameter that it's value is dependent to derivative! the general form of equation is like this (big letter parameters...