Ode Definition and 1000 Threads

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...

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...

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...

If I have y''+y'+2y=sin(x)+cos(x) can I just say y=Ae^{ix} and then find y' and y'' and then plug them in and solve for A. so I get that A= \frac{1}{1+i} then i multiply and divided by the complex conjugate. then I back substitute in Eulers formula. now since I have my...

Well, surely there is one unique solution to linear 1st order ODE and two linearly independent ones for 2nd order linear ODE, but can someone share the proof of this?

hello this question from my coarse notes has been giving me some trouble so i thought i would ask for some help on here, http://img88.imageshack.us/img88/9764/asfar.jpg i understand that since the bases are bases of the same solutions then they are just a multiple of each other, but...

hey guys i've been trying to work out this ode reduction question, http://img204.imageshack.us/img204/8198/asdawt.jpg after i use the hint and end up with a seperable equation then integrate to get \begin{align} & p=\pm \frac{1}{\sqrt{{{y}^{2}}-2c}} \\ &...

Hey, Every where I look I can only find books and pdf talking about the uniqueness and linear independence of the solutions but I haven't been able to find a procedure of finding the solutions to one of these ode's if you haven't been already given a particular solution. I've been trying...

A "simple" nonlinear ode Hi Does anyone see a way to solve/approximate this ODE? dy'=exp(-f(t)y) with y(0)=yo f(t) can be as simple as c*t^3/2 but it may be more complex. This came out as the solution of a very complex problem. This is the final threshold. Thanks, Donifan

Homework Statement Need to solve xy''+y'+xy=0 using Runge Kutta on x[1,3] Couldn't find algorythm to solve second order ODE using this method I know how to do 1st order Homework Equations The Attempt at a Solution I know I have to make this equation into 2 first order ODE...

Hey, I've been trying to solve this ODE using the power series method, y'' + x^2y = 0, I end up with (the first sum can start from 0 or 2, i just left it as starting from n=0) \[\begin{align} & \sum\limits_{n=0\,}^{\infty }{n(n-1){{a}_{n}}{{x}^{n-2}}+}\sum\limits_{n=0}^{\infty...

Homework Statement Find the specified particular solution: (x^2+2y')y'' + 2xy' = 0, y(0)=1, y'(0)=0 Homework Equations The Attempt at a Solution The equation seems amenable to the substitution p=y', so it can be transformed into (x^2 + 2p)p' + 2xp=0, or (x^2 + 2p)dp + 2xpdp=0. Since...

Problem: The following two-dimensional system of ODEs possesses a limit-cycle solution for certain values of the parameter$a$. What is the nature of the Hopf bifurcation that occurs at the critical value of $a$ and state what the critical value is. $\dot{x}=-y+x(a+x^2+(3/2)y^2)$...

How can we solve this ODE with series http://img841.imageshack.us/img841/8682/80858005.png

how can we solve this ODE? http://img818.imageshack.us/img818/3966/59962234.png

I have: $\dot{x}=4x+y-x(x^2+y^2)$ $\dot{y}=4y-x-y(x^2+y^2)$ And I need to find $\dot{r}$ and $\dot{\theta}$ I got as far as: $\dot{x}=r(\text{sin}(\theta)-\text{cos}(\theta)(r^2-4))$ $\dot{y}=r(-\text{sin}(\theta)(r^2-4)-\text{cos}(\theta))$ How do I go from here to $\dot{r}$ and...

Homework Statement I have: \dot{x}=4x+y-x(x^2+y^2) \dot{y}=4y-x-y(x^2+y^2) And I need to find \dot{r} and \dot{\theta} 2. The attempt at a solution I got as far as: \dot{x}=r(\text{sin}(\theta)-\text{cos}(\theta)(r^2-4)) \dot{y}=r(-\text{sin}(\theta)(r^2-4)-\text{cos}(\theta)) How do I...

Homework Statement For the following differential equation: 1) Provide the general solution 2) Discuss for which values of x the solution is defined. 3) Find the solution of the initial value problem y(0) = 3Homework Equations dy/dx = (y+3)(y-5)The Attempt at a Solution 1) so I separate...

Hey, I have been trying to work out how to solve this example question I found in a recommended text, http://img715.imageshack.us/img715/5052/asdavm.jpg Everywhere I've been reading starts with since y=eta(x) is a particular solution then y=eta(x) + u is a general solution, but the...

Homework Statement We are given (1-z)*f'(z)-3*f(z) = 0, f(0) = 2 valid on the open disk centered at 0 with radius 1 and told to prove there is a unique solution to the differential equation. The hint he gave was to find a factor that makes the left side the derivative of a product, but that...

Homework Statement I wanted to solve a ode which has Brownian motion as a variable coefficient Homework Equations 2x2y'' + y' -ρy = 0 where x is the Brownian motion with respect to time ρ is a constant The Attempt at a Solution I have tried power series with no solution. Is there a...

Homework Statement Given the equation mx''+cx=cAsin(Ωt) with the initial conditions x(0)=0 and x'(0)=0. Solve the initial value problem for the case when Ω < ω and show that |x(t)| < H provided A < H(1-(Ω/ω)). Homework Equations The Attempt at a Solution For my solution to...

[Ok so I have transformed a 1st order homogenous ODE into a seperable ODE. However I am having trouble seperating to get y on it's own. Here's the problem: du/dx=(2u^2)/x where u = y/x du/(2u^2)=dx/x <<can't get tex to work -1/(4u^2)=ln(x)+C=ln(Ax) <<can't get tex to work...

I'm not sure where I'm going wrong on this one so I hoped that I could find some help we begin with (x^2 + y^2 + 5) dx - (y+xy) dy taking both partial derivitives I found that 2y (dy) =/ -y(dx) Next I went to find my factor of integration using e^(My - Nx / N) dx)This got me ((1+x)^-3)...

Homework Statement Question According to Newton’s Law of Cooling, the rate at which a substance cools in air is proportional to the difference between the temperature of the substance and that of air. The differential equation is given byAccording to Newton’s Law of Cooling, the rate at which...

Help solving a second order ODE with repeated roots, urgent! I have a differential equaition d2y/dx2 - 6dy/dx + 9y = 0 I have found the general solution to be y = (Ax + B)e3x Now I need to find the solutions to A and B so that... when y = 4, x = 0 when y = 49.e15, x = 5 I...

Ok I'm new to ODE's so yeh, just to double check here's what I've done: Question: Find the general solution to the following differential equation: Equation: y'(x) = sec2 (3x + 1) My answer: Don't I just integrate? So dy/dx = sec2 (3x + 1) then, y = sec2 (3x + 1) dx so y = (tan(3x+1))/3

I have been reading Ordinary Differential Equations (Pollard) from Dover. The chapter I am in, is called Problems Leading to Differential Equations of The First Order - Geometric Problems. Problem : Find the family of curves with the property that the area of the region bounded by the...

Homework Statement I nearly have this problem solved x2d2y/dx2 + 3x*dy/dx + 5y = 8x y(1) = 2, y(exp(pi/4)) = 2sinh(pi/4) I've found the general solution, but I'm not sure how to get the answer with the boundary values Homework Equations The Attempt at a Solution My...

I'm having issues solving a 1st order ODE. Here what happens: NDSolve[{y'[x]/y[x] == k *Pi* r^2* Sqrt[1 + y'[x]^2], y[0] == 136/10}, y[x], {x, 0, 30}] NDSolve::ndnum: Encountered non-numerical value for a derivative at x == 0. Changing the x range is no help... I get the same message for...

Homework Statement I just need to know how to start this. I've never seen a piece wise ODE before and I don't really know where to start to be honest. I know it's non-linear and it's of order one. dy/dx = (1/3)y - 3, y > 0 and dy/dx = -(1/3)y - 3 ≤ 0. y(0) = 1 with y(x) \in C0...

I have to solve this ODE with numerical methods: (y^2 - 1)\frac{dy}{dx}=3y I have no initial conditions to solve it like you would normally do. I am hoping to use a numerical method (Euler... Runge Kutta) to approximate the solution. This is if I solve it using numerical methods right? So, I...

Is there an easy way to show that the system: \begin{align} x_1' &= p_{11} x_1 + p_{12} x_2 + \ldots + p_{1n} x_n \\ x_2' &= p_{21} x_1 + p_{22} x_2 + \ldots + p_{2n} x_n \\ \ldots &= \ldots \\ x_n' &= p_{n1} x_1 + p_{n2} x_2 + \ldots + p_{nn} x_n \end{align} must be equivalent to...

How to solve a equation of this kind T' = a*(T^4 - r^4) + b*(T^4 - s^4) + P*(1 - η(T)) The above equation is driving me nuts... the 'η' is a function of T(Temperature) the efficiency and initial value of T is known. Say at t = 0 T is 298 Need help! Please! I need to find the...

Hey all, there is something that has always bugged me in linear second order ODEs. We say that the general solution is: y=C_1e^{r_1x}+C_2e^{r_2x} where r_1 and r_2 are the solutions of the characteristic polynomial. The cases where r1, r2 are real are pretty straightforward. If they are...

Homework Statement Find the equilibrium points for the following equation. Determine if the equilibrium points are stable and if stable,approximate the angular frequency. (i) d2y/dx2 = cosh(x). Homework Equations The Attempt at a Solution For equilibrium points, do we...

Hi all, I am doing some Laplace Transforms as part of my HND, i have got an answer for this question q' +2q = 5sint q(0)=0, t(0)=0 But i need to prove it by means of using an integrating factor method. My original answer is:- e^-2t +2sint-cost does this look right? I also have...