Second order Definition and 570 Threads

This is from an advanced college physics class, and I'm only in a Calc 1 right now. I've finished the whole problem except for this last part, which deals with a second order differential equation, which I don't know how to do yet. Homework Statement Givens: B, L, A, m, σ, θ (all are...

I am stuck and after several attempts, have made little progress. Homework Statement Solve: (x'-t)x''-x'=0 The Attempt at a Solution I know that the dependent variable x is missing. Therefore, I substitute x'=p and x''=p', giving me, pp'-p't-p=0. However, here I get stuck. If I try to...

Hey folks I'm looking for a way to find the characteristic equation for a second order coupled system of differential equations such as... \ddot{x} + A\dot{y} + Bx = 0 \ddot{y} + C\dot{x} + Dy = 0 Where x and y are functions of time. I know I can solve it by setting x and y to standard...

Homework Statement 22e^{2t}=y''+8y'-9y Homework Equations The Attempt at a Solution The directly previous question to this was the same but homogeneous, i.e. the 22e^(2t) was replaced with a 0. So I know the general solution to the homogeneous ode is C_1e^t+C_2e^{-9t} I know that r(x)=...

Homework Statement 22e^{2t}=y''+8y'-95 Homework Equations The Attempt at a Solution I've been reading a textbook on this and think that I should use "method of undetermined coefficients" I know r(x)=ke^{\gamma*x} so y_p(x)=Ce^{\gamma*x} The trouble is after reading the entire chapter I...

Homework Statement A particular solution of y'' + 4y = tanx Answer choices are: (a) 1/2*cos(2x)ln|sec(2x)+tan(2x)| (b) -1/2*cos(2x)ln|sec(2x)+tan(2x)| (c) 1/2*sin(2x)(ln*cos(x)+x*sec(2x)) (d) 1/2*sin(2x)(ln*cos(x)-x*sec(2x)) (e) none of the above Homework Equations The...

Homework Statement Let z = z (x,y) be a function with x = x(s), y = y(t) satisfying the partial differential equation (Ill write ddz/ddt for the partial derivative of z wrt t and dz/dt for the total derivative of z wrt t, as I have no idea how to use Latex.) ddz/ddt +...

Homework Statement This is NOT a homework problem, but it is similar. Anyway, let's say we have: y''+3y' = 2t^4 This is easy to solve by hand. For the particular solution you get: Yp = At+Bt^2+Ct^3+Dt^4+Et^5 Now, to solve for the coefficients, you can solve them by hand, or you can...

Homework Statement What is the value of a such that the solution of the initial-value problem satisfies limx->infinity y(x) = 0? y''+y'=e^(-x), y(0)=1, y'(0)=a Homework Equations The Attempt at a Solution Not sure what to do with the missing y term... yp=Ae^(-x), y'p=-A^(-x), y''p=A^(-x)...

There seems to be a good source here: http://www.cs.cf.ac.uk/Dave/AI2/node194.html But my problem is understanding the summation. What I am trying to do is calculate ellipticites and orientation angles of images using their second order moments of inertia. My images are in matrix...

Homework Statement Solve ODE of form y''+(2/x)y'=C*(e^y) where C is a constant Homework Equations The Attempt at a Solution I don't really see how to approach this one, so a point in the right direction would be great. Thanks,

What is the difference? I used to assume First order was a Single DOF system and a Second order was a 2 DOF system. Can anyone give me some clarity. Thanks

Hi all, I've come across this forum when searching for solution to my problem and I found that the community is extremely helpful :) I was working on my college project when I came across the equation below. Homework Statement Z = -0.0006*X^2 + 0.0004*X -0.0008*Y^2 - 0.0006*Y + 0.956...

Dear All, I am trying to solve the following system of PDEs \frac{\partial{A}}{\partial{t}}= a_{2}\frac{\partial{{^{2}}A}}{\partial{x^{2}}}-a_{1}\frac{\partial{A}}{\partial{x}}-a_{0}A+b_{0}B \frac{\partial{B}}{\partial{t}}=...

Hi, I am trying to derive the general transfer function for a second order dynamic system, shown below: \frac{Y(s)}{X(s)}=\frac{K\omega_n^2}{s^2+2\zeta\omega_ns+\omega_n^2} In order to do this I am considering a mass-spring-damper system, with an input force of f(t) that satisfies the...

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,

I've tried and failed to search for this on the forum, so apologies if this has been answered many times before. Given a variable u which is a function of x and y: u = u\left(x,y\right)\\ is it possible to solve the pde: Au_{xx} + 2Bu_{xy} + Cu_{yy} = D\\ The knowns are: The real...

Homework Statement i'm supposed to find the general solution of the equation: y'' + 3y' + 2y = e^x + e^-x Homework Equations I have no problem with solving this equation however, i am confused with the step they are taking in the solutions (circled)...

Homework Statement In aerodynamics, one encounters the following initial value problem for Airy’s equations: y''(x) + xy = 0, y(0) = 1, y'(0) = 0 Using the Runge-Kutta method with h=0.005 and determine values between x=0 and x=10 sufficient to sketch the relationship...

Hi, could anyone tell me what methods I would need to solve this system: y\frac{d^2 y}{d\lambda^2}+\left(\frac{dx}{d\lambda}\right)^2-\left(\frac{dy}{d\lambda}\right)^2=0 \frac{y}{2}\frac{d^2x}{d \lambda ^2}-\left(\frac{dx}{d\lambda}\right)\left(\frac{dy}{d\lambda}\right)=0 I...

Hi I need to find the solution of d^2y/dx^2 + 2x(dy/dx) = 0 I've solved it in Maple and get that y=a*erf(x)+b but I have no idea how to arrive at this answer! Any help would be great, thanks.

Homework Statement The circuit below (please see attactment) shows an RLC filter circuit whereby RC = 1/2 and LC = 1/16. Determine the differential equation that describes the relationship beween the input voltage Vi(t) and output voltage Vo(t). If the initial conditions of the capacitor and...

Homework Statement I need to find the solution to x'' + cx' = f(t), for a general f. Homework Equations The Attempt at a Solution Obviously first I solve the homogeneous part to give me A + B*exp(-ct). I also know that the particular solution is written as (1/c)int((1-exp(c(s-t))f(s))ds...

Hi, I have a problem in calculating the second order correlation (coherence) from the master equation for the operators \sigma and a a[+][/SUP] , because I don't know if <aa^{+}a^{+}a> can be factorized to<a><n><a>. I want to do this calculation directly from the density matrix solution. thanks

Homework Statement The equation is x'' - m2x - m2b = 0. m and b are constants. x'' is the second derivative of x, with respect to time. Homework Equations The Attempt at a Solution When I did a differential equations course, I was taught to find the characteristic equation of the differential...

Homework Statement Find the general solution to x'' + e^(-2t)x = 0, where '' = d2/dt2 Homework Equations - The Attempt at a Solution First I did a change of variables: Let u = e^(-t) Then du/dt = -e^(-t) dx/dt = dx/du*du/dt = -e^(-t)*dx/du d2x/dt2 = d/du(dx/dt)du/dt =...

Homework Statement y''(x-1)-xy'+y=x2-2x+1 The Attempt at a Solution I don't even know how to start this, Don't know what substitution to do.

first order system DE --> second order Homework Statement Find a second-order DE for x alone that is equivalent to this system. Homework Equations dx/dt = 2x-y dy/dt = -x The Attempt at a Solution I honestly have no clue where to start; in class we pretty much only stuck to...

Hey, I'm studying Predicate Logic at the moment and I can't seem to wrap my head around the way that english sentences would convert into second order logic. What kind of sentence can be faithfully represented in PL2 but not in PL1? Sorry if this isn't the appropriate section; I'm actually in...

I am a Matlab rookie. I need to solve numerically the following second order differential equations d^2x/dt^2 + w0_(el) * x = e/m_e * E - K3/m_e * x *y; d^2y/dt^2 + w0_(v) * y = - K_3/2M * x^2; I have started to deal with only the harmonic part of the problem. So I tried to solve...

Hi all, I've been doing a lot of thinking and I was wondering precisely how the 2nd order correction to the wave function from perturbation theory is derived: I mean, I can see where bits and pieces come from and I've tried to work through it as an exercise. Does anyone have a...

Homework Statement y''+7y'=392sin(7t)+686cos(7t) with y(0)=4 and y'(0)=9 Homework Equations No real relevant equations The Attempt at a Solution I assumed since the g(t) has function of both sine and cosine the solution would be both the real and non real parts of the solution to...

I could not get LaTex to format properly, so I typed out the question and my work using Microsoft Word's equation editor. Please see the attached document, apologies for any inconvenience! These problems involve the techniques for the method of undetermined coefficients and variation of parameters.

Hello forum, I am trying to solve a differential equation for the last four hours and I can't figure out how... here it is \frac{d^2x(t)}{dt^2} + \frac{dx(t)}{dt} + c x(t) = d e^{-a t^2} actually my problem is how to handle the Gaussian term... if anyone can help please...

Hello all, I'm having a little trouble getting the Latex to work, so I'm hoping this won't be too hard for everyone to understand. Homework Statement I am given the second order differential equation x2*y''(x)+(2*b+1)*x*y'(x)+c*y(x) = 0 Use the transform x=ez to find the general solution...

Homework Statement Solve the IVP, \frac{1}{4}y'' + 16y = 0 y(0)=\frac{1}{4} y'(0)=0 Answer is given... y(t) = \frac{1}{4}cos 8t Homework Equations The Attempt at a Solution This has the characteristic equation \frac{1}{4} \lambda^2 +16\lambda=0 Solving for lambda, I got...

This is a concept question i was wondering. in what instances would this be true and in what instances would this be false. im in general chem 2.

Hi, i need help solving this equation: y'' + 4y' + 4y = 0 any help is appreciated!

Homework Statement Let V denote a vector space of twice differentiable functions on R. Define a linear map L on V by the formula: L(u)=au''+bu'+cu Suppose that u_{1},u_{2} is a basis for the solution space of L(u)=0. Find a basis for the solution space of the fourth order equation L(L(u))=0...

Homework Statement Here is my issue. I am an EE student that has been part time for almost five years. I took diff eq and signals a long time ago. I am currently taking a feedback and controls class, and my lack of memory in these topics is killing my study time. I am looking for relevant...

Could you please help me or give me any hint to solve this ODE.. \frac{d^2y}{d x^2} + ( 2\rm{sech}^2 x - a^2 ) y = 0 where a is a constant. I want only even function solution. (y(x) = y(-x)) BTW, this is a homework problem. I encountered this equation while considering surface waves...

I'm trying to solve equation in the attached pdf, which describes anistropic diffusion in 3D with an additional term to account for hydrogen bonding and unbonding of the diffusing substance to the medium. I've considered Laplace transforms, then solving in the Laplace domain, then inverting...

Homework Statement Evaluate \int^{2\pi}_{0}\frac{1}{r}\frac{d^{2}f}{d\varphi^{2}}d\varphi Homework Equations n/a The Attempt at a Solution I get the integral as \frac{1}{r}\frac{df}{d\varphi} Not sure how to evaluate this.

Hey guys, I am new to PF. I need to be able to model a stiff differential equation in MatLab. I haven't used MatLab before so I am not really sure how to set the function and boundary conditions for the equation: y'' + (2/x)*Y' = (.7/x^2)*( (y^(-1/2)) - (.067)((1-y)^(-1/2) ) y(0)=0...

Hi guy, I have this ODE that I'm having problems with y"+4y'+4y= e^(-2x)logx Now, Using method of UC to get rid of the RHS I've tried using Ae^(-2x) x^2 logx However, I'm not quite sure whether that is correct or not as I have never had a question containing logs before

Hi, I have a differential equation of the form d2 x ---------------- = g/z * x(t) dt2 Here g and z are constants. So, this is a 2nd order ODE which has a closed form solution. In fact, i know the solution for x in terms of cosh and sinh functions. In the above differential...

Hi. I believe I understand separation of variables for a first order DE. But can anyone tell me how to use it on a second order DE? In particular I have been looking at this example http://en.wikipedia.org/wiki/Integrating_factor#General_use" where it is claimed that one can use separation of...

Homework Statement Derive the second order differential equation relating x(t) and y(t). Using the Laplace transform, find the total response as a function of the zero input response and the zero state response in the following form.Homework Equations Y(s)=Yzs(s) + Yzi(s) The Attempt at a...

Homework Statement d2y/dx2-dy/dx+y*exp(2x) = x*exp(2x)-1 substitute t=exp(x) and set z(t)=y(x) and rewrite hence find all solutions The Attempt at a Solution Rewriting gives: d2z/dt2-dz/dt+z*t^2=(ln(t) * t^2) - 1 however I don't see how this in any way helps us...

Hi, I'm trying to solve this exercise: 0=<x=<a D*C''(x)= A*C(x)/ [K+C(x)] D, A and K are constants and we know the following IV: C(0)= Known (number) C''(a)=0 Do you have any idea how I may proceed with this?