Odes Definition and 227 Threads

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...

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.

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...

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...

Consider the system of linear differential equations: X' = AX where X is a column vector (of functions) and A is coefficient matrix. We could just as well consider a first order specific case: y'(x) = C(x)y We know that the soltuion will be a subset of the vector space of continuous...

So how do I show that when we have a linear second-order differential equation expressed in self adjoint form that the Wronskian W(y1,y2)= C/p(x) W=y1y2'-y1'y2, and C is a constant, and p is the coefficient where Ly=d^2/dx^2(pu) - d/dx(p1u) +p2u ? I know Ly1=0 and Ly2= 0 if that helps at all.

I'm dealing with systems of 3 differential equations that are all coupled to each other. Fortunately, all the ODEs are first order. Can somebody give me a primer of how to use matrices to solve these problems? here's an example: Say we have a system of 3 ODEs all coupled to each other...

Hello and thanks in advance for anyone who can help at all. I have two problems that have stumped me.. I'm in an advanced ODE class. Here they are: 1) Consider the first order ODE f_a(x) where a is a parameter; let f_a(x0) = 0 for some solution x0 and also let f'_a(x0) != 0. Prove that...