Odes Definition and 227 Threads

Given the ODE of the form: y''(x) + A*y'(x) + B*y(x) = 0 If we choose a solution such that y(x) = e^{mx} and plug it into the original ODE, the ODE becomes: (m^{2} + A*m + B)e^{mx} = 0 If we solve for the roots of the characteristic equation such that m = r_{1}, r_{2} (root 1 and root 2...

This is not a homework problem, I just want to understand some theory behind this mathematical method. Specifically, if we know that one solution is y1(t), then why is the second solution in the form y2(t) = v(t) * y1(t)? Where v(t) is the function that you need to solve for. Why does...

Consider a three-tank system modeled by the equations: x_1' = -5x_1+5x_3 x_2' = 5x_1-2x_2 x_3' = 2x_2-5x_3 (A) Initially there are 10 pounds of grain in each tank. What will the amounts be as t \rightarrow \infty? (B) Solve the system and verify your conclusion from (A). I'm...

I was wondering what a guess would be for the particular solution of the right hand side of an equation if it looked like this: x^{2}y" - 4xy' + 6y = ln(x) My textbook has some specific examples of the right side function along with the corresponding form of the particular solution...

Given $x''-x+x^3+\gamma x' = 0$. Is the below correct? Can I do this? The answer is yes. Let $x_1 = x$ and $x_2 = x'$. Then $x_1' = x_2$. \begin{alignat}{3} x_1' & = & x_2\\ x_2' & = & x_1 - x_1^3 + \gamma x_2 \end{alignat} Then I have the above linear system from the given ODE.

First create the function file and name it whatever you would like. I prefer phase-portrait. % Phase Plot Program % To use this function, do the following: % >> phase_portrait(x1, x2, y1, y2, tfinal, 'F', N); for example, % >> phase_portrait(-5, 5, -5, 5, 10, 'F', 5)function [] =...

My question is in regards to systems of ordinary differential equations. One of my research topics right now involves working with some complicated coupled ODEs used to model ecological stuff. Without getting into the details, the model I am working on now has a bad tendency to diverge for...

Is there a resource that is just a walkthrough of various kinds of problems one might get and the ways to solve them? I'm not talking about the basics from the calc and difEQ series (u substitution, partial fraction decomposition, trig substitutions, trig power reduction, integration by parts...

Just checking a solution. $y' = \begin{pmatrix}4 & -1\\ 2 & 1\end{pmatrix}y $ $$ \lambda^2 - 5\lambda + 6 = (\lambda - 3)(\lambda - 2) = 0. $$ So the eigenvalues are $\lambda_1 = 3$ and $\lambda_2 = 2$. To find the eigenvectors, we must solve $(4 - \lambda)y_1 - y_2 = 0\iff y_2 = (4 -...

Hello All, I am new to this community but by reviwwing the questions and answers posted in this forum I was encouraged to share my question with you and I hope you can help me. I have a system of 4th order ordinary differential equations for several functions which I call them: y_1,y_2...

Hi all, first of all, I have to admit I have often used this richness of knowledge that permeates through the posts of this forum to find answers to questions that I have come across in my studies. Thanks for all! Now, I have a question to post, for the first time. I am trying to teach...

I was wondering what the common methods for solving such a system are: 2 m \ddot{x} - m l \ddot{θ} θ + k x = 0 m l^{2} \ddot{θ} - m l \ddot{x} θ + m g l θ = 0

I'm at a loss on this question...my troubles seem to be algebraic or that I'm simply missing something.x' = \mu - x2 +4x4 my method for these questions has basically been to do everything required to draw bifurcation diagram bar drawing the actual diagram itself (ie, find equilibria, what...

I have previously taken PDE's and ODE's. I understand obtaining the equation y''+lambda*y=0 (lambda then giving the eigenvalues). But I've encountered now the use of eigenfunction expansion for an ODE; and what I don't understand, is that in solving it they're making some assumption that y''+y=0...

I'm running into a problem. This is mainly for reading over the summer and I'm working on getting through a dynamical systems book on my own. I've come across a system that I'm not too sure on the procedure. Consider the following system of differential equations: \frac{dX}{dt} = 1 - X -...

hello, I am going through the first chapter (a review chapter) of a second-course book in ODEs, and can't seem to remember how to re-write higher order DEs into a system of first order linear ODEs, and my old textbook only shows this for second order equations... The question is: "Write the...

I got some questions about this topic... y'' + p(z)y' + q(z)y=0 where y (and its derivatives) is a function of z, z ∈ ℂ. 1) My books says this: In points where both p(z) and q(z) are analytic, y(z) is also analytic. But in points where p(z) or q(z) (or both) aren't analytic, y(z) may not...

Hello Comming from Discrete Mathematics, I have very little knowledge in Solving ODEs: I have the following equation (where E(x) is an ordinary generating function). E'(x) = \frac{(E(x)*E(x) +E(x)-x)}{2x*E(x)} with E(0) = 0 Is there any hope to solve this equation?

Homework Statement Out of a set of differential equations with boundary conditions, there are three (first order) equations I couldn't solve. These are: Homework Equations 1. \frac {dy} {dx} = \sqrt{x + y}, y(1) = 0. 2. \frac {dy} {dx} = 2y(x \sqrt{y} - 1), y(0) = 1. 3. 2x^2...

Homework Statement F(s) = s/((s-1)(s^2+1)) F(s) = (s/(s^2+4s+5))(e^(-3s)) Homework Equations Don't believe there are any. The Attempt at a Solution Not particularly sure. I can solve ((s-2)(e^-s))/(s^2-4s+3), but seem to be having problems with these.

do you have a idea about it?can you help me http://img17.imageshack.us/img17/1156/18176658.png

Right now I'm a sophomore at a state uni with hopes of getting into graduate school in pure mathematics. When I was a freshman, I surveyed the three major areas of math - analysis, algebra, and topology - and I decided that analysis was for me. Although I did very well in Algebra, I found it...

I have a system of coupled ODEs which tells the propagation of power Pi in an optic fiber. \frac{\partial P_i }{\partial z} = \left (N\sigma - 1 \right ) P_i where N = \frac{\sum_i \alpha_i P_i}{\sum_i \beta_i P_i + 1} If the signals are copropagating, there is no problem since...

Homework Statement Consider the following initial value problem for two functions y(x),z(x): 0 = y''+(y'+7y)\text{arctan}(z) 5z' = x^2+y^2+z^2 where 0 \leqslant x \leqslant 2,\; y(0)=1.8,\;y'(0)=-2.6,\;z(0)=0.7. Rewrite the system of ODEs in standard form using a suitable substitution...

Integrating Factors for ODEs (Question from Boas) Find an integrating factor by inspection to make the below differential equation exact. (y^2-xy)dx+(x^2+xy)dy=0 I've been inspecting, but I'm not seeing it! Is there a way to analyze this in my head that will lead me more easily to the...

Hi, Usually, it takes a while for me to digest information, because I have a lot of filters in my mind and to remember and understand things I have to put all the new information in context. I have to have an interpretation of the content. For this reasons I am doing terribly in my ODE course...

If ay+b\int^y_0ydy+cy'=0 then ay'+by+cy''=0 now, let y=e^{sx} thus, s^2+a/cs+b/c=0 and then one solves for s. It is then plugged into what sources are deeming a "general solution" y=C_1e^{s_1x}+C_2e^{s_2x} however, none of these texbooks explain or derive where this comes from, and I have not...

Hi everybody, I've troubles with the following two systems of differential equations: image hosting gif I tried to reduce the order but I wasn't able to do anything...

Suppose we have some ODE given by y' = G(x,y)/H(x,y). Let x and y depend on a third variable, t, so that x and y are parametrized in a way. Then applying the chain rule to y' gives \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{G(x,y)}{H(x,y)} Then comparing the numerators and...

Homework Statement Say you have: EQ1: y1''*t+y1'*t+y2=0 and EQ2: y2''*t+y2'*t+y1=0 y1(0)=0,y1'(0)=0,y2(0)=0,y2'(0)=0 Homework Equations The Attempt at a Solution I can get it so far, but having both y1 and y2 really gives me fits: Eq1: Y1(-2s-1)+dY1/ds(-s2-s)=-Y2...

Given an ODE in the form of f(t)y''+g(t)y'+h(t)y=0 If all I am looking for is the y(t) at a specific value of t and NOT the general solution, can I just plug in that value of t into the original ODE and then solve it analytically or is a numeric solution the only way?

Homework Statement Use eigenvalues and eigenvectors to find the general solution of the system of ODEs.. x1 = 3x1 - x2 x2 = -x1 + 2x2 - x3 x3 = -x2 + 3x3 Homework Equations The Attempt at a Solution I converted that into the matrix...

Homework Statement y'' + 2y' + y = f(t); y0=y0'=0 f(t) is piecewise -- 1 for 0 < t < a; 0 for t > a Use y(t) = ∫G(t,t') f(t') dt' with bounds 0 to infinity 2. The attempt at a solution I don't really have any logical attempt. My highest math is diffy q 1, Calc 3 and LA 1, I...

I'm having a problem with NDSolve. See attached picture. I have a package generating a set of ODE's, which I display, and then the next line is the NDSolve integration. I get an "Encountered non-numerical value for a derivative at t==0" error, and I can't spot the mistake. The one thing that...

Okay, I'm going insane. I have these problems completely worked out and have stared at them for centuries but the online homework is still telling me they're wrong. Could anyone here take a look and let me know? I'd appreciate it a ton. [SIZE="4"]Problem 1: Exact Equation Homework...

Homework Statement If the population y of rats on a farm at time t (in weeks) satisfies: dy/dt = -y(y-100)/50 then how many rats per week should be killed to eradicate the population? Homework Equations None known. The Attempt at a Solution The ODE dy/dt is autonomous, so I can...

Hi! I think I have to ask this since I'm having health problems- from Kreyszig, for xy'=-y how do you verify the solution y=h(x)=clnx by differentiating y'=h'(x)=-clnx^2? I don't see how you get the x^2 term also for ODEs the solution is on an open interval a<x<b but how does it include...

I'm trying to optimize a system of 10-20 differential equations in Matlab using a genetic algorithm. The problem is, when I call the ode function, whether it be ode45, ode23, ode15, etc., it sometimes gets stuck in an infinite loop. The genetic algorithm no longer progresses and I have to Ctrl+C...

Homework Statement so I'm trying to find the general solution of this problem: \mathbf {x'} = \begin{bmatrix} 2 & 0\\0 & 2\end{bmatrix}\mathbf{x} Homework Equations det(A- rI) = 0 The Attempt at a Solution det(A - rI) = det \begin{bmatrix} 2-r & 0 \\ 0 & 2-r \end{bmatrix} =...

What kind of systems do ODEs describe? What kind of systems do PDEs describe?

Assuming knowledge of homogeneous ODEs and nonhomogeneous ODEs that can be made homogeneous (eg, y'-y=x), how does one solve those that cannot be made homogeneous (eg, y'-y=cosx, y''-xy'+y=0, cos(y'')+sin(y')=0)? EDIT: Maybe "made homogeneous" is the wrong way to put it... By being able to be...

Homework Statement Consider the IVP compromising the ODE. dy/dx = sin(y) subject to the initial condition y(X) = Y Without solving the problem, decide if this initial value problem is guaranteed to have a unique solution. If it does, determine whether the existence of that solution is...

Hi, could someone please link me to the relevant theorems etc (or explain personally) that answer the issue that follows. Say you have an ODE (let's say 2nd order for now). Let's look for a power series solution (ie assume we're engineers). So, we write out a couple of sigmas etc and sub...

Homework Statement (2xy-5)dx+(x^2+y^2)dy=0, y(3)=1 (2x+y^2)dx+4xy dy=0, y(1)=1 x^3y'+xy=x, y(1)=2 y'(t)=-4y+6y^3 We're doing these in 2nd yr engineering Math and I have heard the Lecturer say they are useful across all disciplines. I've heard him suggest RLC circuits, springs with...

Matrix Systems of ODEs -- Mathematica I'm trying to solve the classic "systemm of linear ODEs" of the form: Y(t)' = X*Y(t) Its homogenous, so it wouldn't hurt to rewrite it as Y(t)' - X*Y(t) = 0 (if that helps?) so here is my attempt at the solution solExp == NDSolve[Y'[t] ==...

Can anyone please suggest whether I can use MATLAB ode45 for the numerical solution of the following equations? mx ̈+ c_x x ̇ + k_x x= F_x0+ μ(v_r ) (K 〖VB〗^2 y ̇/v) sgn(v_r ) my ̈+ c_y y ̇+ k_y y= F_y0+ (K 〖VB〗^2 (y/v) ̇ ) Where, m, c_x, k_x, c_y, k_y, F_x0, F_y0, K, v are known...

i have a question but no mark scheme so i can't see where I am going wrong. a mass, m, is dropped with speed zero from point O at time t=0 after time t it has traveled x. the body is subject to acceleration due to gravity and drag -mkv. (A) write the equation of motion: ok so i know...

Attempting Problem 1 of Arnold: ODEs, Ch. 1, section 2.2, it seems I'm not understanding something pretty basic about what he means by "the solution of a differential equation". This is the kind of equation he's talking about: \dot{x} = \mathbf{v}(x) \enspace\enspace\enspace (1) where, if...

I'm reading Arnold: Ordinary Differential Equations, Chapter 1. In section 1.2, an integral curve was defined as the graph, in the extended phase space, \mathbb{R} \times M, of the motion \phi : \mathbb{R} \rightarrow M of a phase point in M. In 2.2, an integral curve is defined as the graph of...

Hey, I feel kind of stupid for asking this, but how does one solve an ODE of the form y'' = 0 I know it's Ax+B=0 but I forgot how I got there. Cheers,