Odes Definition and 255 Threads

Wave equation with inhomogeneous boundary conditions Sorry about the thread title, I've tried changing it but it won't work. Homework Statement Solve the wave equation (1) on the region 0<x<2 subject to the boundary conditions (2) and the initial condition (3) by separation of...

I don't understand what is happening in the following problem. What happens to ln when it moves to the RHS? Why are there two exponential functions on the RHS and why is e^c made to equal A? http://users.on.net/~rohanlal/mathproblemln.jpg

Homework Statement y"+3y'+2y= sin x y(0)=0 y'(0)=1 Evaluate y(0.1) Homework Equations Power Series Equation The Attempt at a Solution

Homework Statement Find all values of a for which all solutions of y''(x) + (a/x)y'(x) + (5/2)y(x) = 0 tend to zero as x tends 0+ and all values for which all solutions tend to zero as x tends to + Homework Equations The Attempt at a Solution I am not even sure where to being with this...

Hello, I have been trying to solve this problem and the only thing I got is errors and errors. Also I need to plot y versus t, y' versus t and y' versus y?? Homework Statement The system of ODEs y1'= y2 y2'= -2y1-0.03y13 The time span is [0:0.1:5] and there are no initial...

Homework Statement I have a problem with a nonlinear ODE, but this is my first time at using the forum. Can anyone tell me how I can introduce equations into the thread. I have MS Word which allows me to generate equations in a document. Is there a way I can stream an MS Word document into a...

I am required to solve the following system of ODEs numerically. Could someone suggest an appropriate methodology. These equations are phenomenological equations derived from irreversible thermodynamics. I have to solve for the flux terms given on the L.H.S. The coefficients of differentials on...

Homework Statement Solve the following problems using Laplace Transforms: y' - y = 2e^t, y_0 = 3 y'' + 4y' + 4y = e^{-2t}, y_0 = 0, y_0' = 4 y'' + y = sin(t), y_0 = 1, y_0' = 0 y'' + y = sin(t), y_0 = 1, y_0' = -\frac{1}{2} Homework Equations N/A The Attempt at...

Let's suppose I know every coefficients this script: and y1 alfa y2 v y3 A y4 T function dy=isaacsimply(s,y) dy = zeros(4,1) global ... dy(1)=(Cd_for*q_inf*h*(sin(y(1)))^2+... g*y(3)*(rho-rho_inf)*cos(y(1))... +E*U_inf*sin(y(3)))/... (-rho*y(3)*y(2)^2); %dalfa...

I am trying to model a packed bed distillation column for a binary liquid in Python. Unfortunately, when I set up my system, I end up with a system of coupled non-linear first order ODEs with boundary conditions at opposite ends (feed conditions and exit conditions), and I do not know how to...

Analytical Solution to this? -- linear system of ODES Hi All, It's been awhile since I've even attempted to solve something analytically, so before jumping back into the text. Does the following already have a common solution that I can find somewhere? Thanks, dx1/dt = A1 + B1x1...

Hi there, I have yet another Matlab query. I have an m=file that I am using to solve an ode. This file has a constant (call it H) within the differential and when I use the ode solver in the command window returns values of z and r (this returns two 85x1 vectors which can be plotted...

infinite series solution for NON-linear ODEs? Is it possible to use the infinite series method (Frobenius) to obtain general solutions of non-linear ODE's, I want to try a second order equation. Any good references where I can see how that goes exactly?

here is a simplified version of my working equtions y''' = \frac{(y'' y+y' y) y + y'y''}{y' + y''} and 3 related boundary conditions, is there some hints to solve such equation numerically? ThX

Okay, I know that this is probably a simple question but I've always been good at doing the complicated things and bad at doing the easy things :D Here's what I've got: Find the general solution for the system of coupled ODEs. Determine kind and stability of the critical point. Sketch phase...

Hi, it is well known that a second order ODe can be transformed into a system of two ODEs through the transformation u=y', v= y. Is the other way round possible? I mean, I have a system of 2 ODEs and want to transform it into a sucession on higher order problems that can be solved one after...

Hello everybody! Here are two ODE 2nd order I tried to solve, but I failed :( r''[t] - k/(r[t])^2 = 0 xy''[x] = ay[x] + b Could anyone of you please help me? Thanks in advance :)

Homework Statement I'm trying to understand the Variation of Parameters in ODEs and I came up to this following expression which i cannot solve: {2\,{e}^{-t}{e}^{-3\,t}\choose {e}^{-t}{e}^{-3\,t}} \int {\,{e}^{t} {e}^{\,t}\choose {e}^{3t}{2e}^{-3\,t}} {10\,\cos \left( t \right)...

Homework Statement I have two questions: 1) If i have two first order ODE y(1) and y(2) (in terms of time), i know how to plot y(1) versus time and y(2) versus time but i don't know how to plot y(2) versus y(1) 2)I have two second order ODES X''=... and Z''=... to solve this, we make the...

Homework Statement I have two questions: 1) If i have two first order ODE y(1) and y(2) (in terms of time), i know how to plot y(1) versus time and y(2) versus time but i don't know how to plot y(2) versus y(1) 2)I have two second order ODES X''=... and Z''=... to solve this, we make the...

Anyone have much knowledge on the ODE solvers in matlab? I have an ODE and I want to specificy whether the input is time or the y value for the dy/dt problem.

Suppose I already have a solution u to a first order ODE. If I try to solve this ODE without initial conditions and I get another solution w, then it can be regarded as a function of an arbitrary constant: w=w(C). Is it true to say that u = w(C) for some C? If so, how do I find such a C?

Hi, I want to analyze a system of ODEs arising in biology of the form: x'=a1*x*z y'=b1*x + b2*y z'=c1 + c2*z + c3*y*z with x,y,z state variables and a1,b1,b2,c1,c2,c3 constant parameters. The difference to a linear system of diffs eqs. is that two state variables are multiplied...

Hi, Can anyone please tell me how to go about solving this system of coupled ODEs.? 1) (-)(lambda) + vH''' = -2HH' +(H')^2 - G^2 2) vG'' = 2H'G - 2G'H lambda and v are constants. And the boundary conditions given are H(0) = H(d) = 0 H'(0) = omega * ( c1 * H''(0) + c2 * H'''(0) )...

1.The position of a particle x(t) obeys the following differential equation d^2x/dt^2 + 4(dx/dt) + 3x = (3t/2) -4 If at t=0, both x=0 and dt/dx=0, find x(t) Attempt at solution I've found the homogeneous solution to be y=Aexp(-3x) + Bexp(-x), and know how to find x(t) given...

I have a couple ODEs that I need to solve. I was probably just going to put them into mathematica, but I like finding the analytical way also. The first one is \frac{d}{dx}\left( \frac{(y + \lambda)y'}{\sqrt{1+y'^2}} \right) = \sqrt{1+y'^2} Lambda is a constant and y' is dy/dx. I...

Homework Statement It's been a couple years since diff. eq. Any tips/strategies on solving the first-order ODE: K\frac{dp(t)}{dt} + \frac{p(t)}{R} = Q_0 \sin{(2\pi t)} where K, R and Q_0 are constants?

Now I am reading over a theorem, which is very easy to understand, except for a small caveat. Bascally: A set of functions are said to be linearly dependent on an interval I if there exists constants, c1, c2...cn, not all zero, such that c1f1(x) + c2f2(x) ... + cnfn(x) = 0 Well the...

I'm just curious as to what the actual distinction means. I understand that the requirement for a linear ODE, is for all the coefficients to be functions of x (independent variable), and that all derivatives or y's (dependent variable) must be of degree one, but that doesn't tell me much...

Normally I can do these, and I'm fairly familiar with the equations used here, but for the life of me I can't figure this one out. Here's the question: The following equation is the known as Blasius boundary layer equation for the laminar flow over a flat plate in similarity variables: 2f''' +...

Hi, can someone please help me do the following question? Q. A light elastic string of length 3l is stretched between two fixed points a distance of 3L apart (3L > 3l), and two particles, each of mass m, are attached to the string, one at each of the two points of trisection, The system is...

y''-6xy'+(6x^2-2)y=0 y_{1} = _____________ I have to solve the above equation using power series.. but I am stuck. What I have so far is: y=\sum_{m=0}^\infty a_{m}x^{m} y'=\sum_{m=1}^\infty ma_{m}x^{m-1} y''=\sum_{m=2}^\infty m(m-1)a_{m}x^{m-2} = \sum_{m=0}^\infty...

I am asking this question as it relates to physics, and in particular how it relates to harmonic oscillation. Why is the equation not solved when I use only a particular solution? Why is the equation not solved when I use only a general solution?

I have a quick question. For a project that I'm doing, I need to numerically solve systems of nonlinear differential equations. Can anyone suggest a numerical method which I could code as a short C program? Thanks.

Hi, Please can someone help me on how to do this exercise. Give a fundamental matrix for the system: {x'(t)=-y(t) {y'(t)=20x(t)-4y(t) the solution is like: {v1(t)=e2t*cos(4t)[1;4]+e2t*sin(4t)[-1;-2], v2(t)=e2t*cos(4t)[1;4]+e2t*sin(4t)[0;-4]} [1;4]...are colunm vectors. IT is just...

Given:Second order ODE: x" + 2x' + 3x = 0 Find: a) Write equation as first order ODE b) Apply eigenvalue method to find general soln Solution: Part a, is easy a) y' = -2y - 3x now, how do I do part b? Do I solve it as a [1x2] matrix?

I've learned the basic methods of ODEs but I'm looking for a more advanced book, covering things like limit cycles, existence and uniqeness thoerems, phase portraits, and so on. Does anyone know of a good book for such topics.

Hi, I have a system of three coupled nonlinear ODEs: \frac{d}{du}(nu)=exp(-\phi), u\frac{du}{dx}=\frac{d\phi}{dx}-\frac{u}{n}exp(-\phi), \frac{d^2 \phi}{dx^2}=n-exp(-\phi), with boundary conditions \phi=\phi'=u=n=0 \text{ at } x=0 Does anyone know, or have references...

I'm using the method of undetermined coefficients here, but I'm either not making the correct ansatz or I'm just confused on the method. The problem is 2y'' + 3y' + y = t^2. I gussed Y = At^2. Is this correct? It doesn't solve the differential equation, which is the only check I know...

:-p Hi all, I'm new here and was wondering whether anyone could give me a hint on the following two problems about ODEs (oh...and also, can anyone tell me where can I find this formula editor?): Problem 1 find the solution for dy/dx + y = y^2 (cosx - sinx) try substitution: f...

Hi all, I'd be happy if someone could clarify these two things to me: 1. While solving linear first-order ODE, I first solve homogenous equation (with the right side equal to 0) and eventually I get to the point (just an example): \log |y| = \log C(e^{x} - 1) Now, is it ok to compute C for...

Let's say I assumed that the answer to a PDE was U(x,t)= XT, where X,T are functions. I then further my answer by getting to a point for T'/T=kX''/X, where k is some constant given in the boundary conditions. I then continue by working on either side to find each function. Suppose I work on...

i know the solution to a system of trhee odes of the form div(xy)= C1 (1) xy grad(y) = -grad(z) -C1y (2) div(xy(y^2/2+ C2 z/x))=C3 (3) where x, y, and z are functions of r only, (spherical simmetry) and div F= (1/r^2) d (r^2F)/dr, and...

Hi, I have never had to handle ODEs where the coefficients are complex. Just wondering if solving this is even possible and whether you can point me to any sources/books. Say I had the ODE (df/dx) + a.f^2 + (b+i)f + c = 0 where f(x) is a function of x, a, b and c are constants, and i...

In order to solve this pde that I'm on, I must solve this system of odes, \frac{dx}{dt} = -y and \frac{dy}{dt} = x , which doesn't look bad, but I haven't had a second semester of ode yet where systems of differential equations are covered. How is this solved?

Does anyone know how to graph the integral curves / slope fields of ODEs on the 89? I don't have a manual for mine, and suppose a few of you are quite familiar with it. Thanks in advance.

Hi, I've been working on some ODEs and I've been using all of the standard techniques. Recently, I came across some solutions to some IVP problems(I don't have the questions, only the solutions). I'm curious as to the motivation behind the follow technique. As in, why would this method be used...

I was reading something about ODEs and I came across a section which discusses the generalisation of first-order isobaric equations to equations of general order n. The definition I have is that an n-th order isobaric equation is one in which every term can be made dimensionally consistent upon...

Hi, I'm wondering if anyone has recommendations for textbooks which cover the basics of ODEs. I'm looking for books which cover first and second order ODEs and related topics.

Can anyone help me figure out how to model this pendulum system using ODE's? It is a two-mass system in which the two masses are placed at opposite ends of a massless rod, with a fulcrum somewhere in the middle. The smaller mass is length k away from the fulcrum and the larger mass is length L...