Ode Definition and 1000 Threads

Homework Statement I have the ODE y' = f(\frac{y}{x}) , and I want to re-write this as a separable equation using the change of variable u = \frac{y}{x} The Attempt at a Solution I use the chain rule to write y' = \frac{dy}{dx} = \frac{dy}{du}\frac{du}{dx} = \frac{dy}{du}(-\frac{y}{x^2})...

Hi all Quick one, if one had an equation y' = x on could simply separate the variables and integrate. Now it the equation y'' = x you would use separation of variables what drives this? Also y'' =0. Is the same as. y''dx =0 dx Why is this legal?Thanks in advance

Homework Statement Solve the piecewise linear ODE, y' - y = f(x), y(0) = 1, where f(x) = 1 when 0<=x<=1 and f(x) = -1 when x > 1. y(2) = ? Homework Equations None The Attempt at a Solution I found the integrating factor to be e^-x and multiplied both sides of the equation by the...

$y''+y=\alpha\cos x + \cos^3x$ What value of $\alpha$ makes this resonance free? $\cos^3 x = \frac{1}{4}\cos 3x+\frac{3}{4}\cos x$ So $y''+y=(\alpha+\frac{3}{4})\cos x + \frac{1}{4}\cos 3x$ What am I supposed to do to find alpha?

Homework Statement I want to find the general solution for y(x) if dy/dx = x + y^2 with initial cond't y(1) = 2 Homework Equations The Attempt at a Solution I can't figure out how to make it linear. (Obviously I don't think it's seperable) Any suggestions/solutions...

$y' = \begin{pmatrix}1 & 2\\ 0 & 1\end{pmatrix}y$ The characteristic equation is $$ \lambda^2 - 2\lambda + 1 = (\lambda - 1)^2 = 0. $$ So the eigenvalues are $\lambda_{1,2} = 1$. Solving $(1 - \lambda)y_1 + 2y_2 = 0\iff y_2 = -\dfrac{1}{2}(1 - \lambda)y_1$, we have $$ y = \begin{pmatrix} 1\\...

$y''+y = e^{it}+e^{3it}$ Solution $y = Ae^{it}-\dfrac{1}{8}e^{3it}-\dfrac{it}{2}e^{it}$ and $y''+4y=1+\sin t+\sin 2t$ Solution $y=A\cos 2t + B\sin 2t + \dfrac{1}{4} + \dfrac{1}{3}\sin t - \dfrac{t}{4}\cos 2t$ Correct?

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...