Second order Definition and 570 Threads

I think I know how to solve \frac{d\vec{x}}{dt}= A \vec{x} where A is a constant nXn matrix. We just compute the eigenvalues and the corresponding eigenvectors. But how do we solve \frac{d^2\vec{x}}{dt^2}= A \vec{x} Can we say straight away that the solution is...

Homework Statement find the general solution to the second order ode: x4y''+2x3y'+y=0 Homework Equations using Euler's method The Attempt at a Solution assume that the solution is y=xa then y'=axa-1 and y''-a(a-1)xa-2 substituting these into the ode: a(a-1)xa+2axa+xax-2=0...

Homework Statement Monochromatic light strikes a diffraction grating at normal incidence before illuminating a screen 1.99 m away. If the first-order maxima are separated by 1.36 m on the screen, what is the distance between the two second-order maxima? Homework Equations I think these...

Dear Friends i am lookin g for the solution for second order differential equation. will anyone please help me to solve this problem.

Homework Statement I'm not sure if this is actually solvable, or a typo on my homework... but here's the problem in question: Solve the ODE: \frac{d^{2}y}{dt^{2}} + t^{2} \frac{dy}{dt} + y^{2} = 0, y(0)=0, y'(0)=0Attempt at solution I've been stumped on where to even start with this one, but...

I am not able to find the general integral of the following non-linear 2nd order equation: y^2 y'' + a y^3 - b = 0 in which: y = f(x) 0 < a <= 1, is a constant b > 0 , is a constant.

Hi I'v got a maths exam on Tuesday for my 2nd year of chemial engineering. Been going through a past paper and have been going over 2nd order homogenous DE's Im at the stage of calculating the roots (wether repeated or 2 distinct roots) I take the easy path like so: E.g m2 + 4m + 4 =...

Homework Statement Suppose that L is a second order linear differential operator over the interval J, that f is a function defined on J, and that the function v has the property that Lv = f on J (a) Show that if y = u + v and that Lu = 0 on J, then Ly = f on J (b) Show that if Ly = f on...

Homework Statement 4xy'' + 2y' + y = 0 2. The attempt at a solution In class, we were given that y1 = c1Cos(\sqrt{}x). We then used reduction of order to figure out the other solution Yet, I've been trying to figure out, is how do you get y1 in the first place? To me, it doesn't...

I hope this is the right place to post this question. I'm trying to figure out how to run a numeric integration for a nonlinear second order ODE with Neumann B.C. I've started programming up Runge Kutta 4, but clearly without a boundary condition on the function, but only on its derivative...

Homework Statement y''+16y=9xe^(4x) y(0)=0 y'(0)=0 find the solution, y(x) to the differential equation The Attempt at a Solution I found the particular solution to the right side of the equation, which is correct, yp= .28125x-.0703125e^(4x) For the left hand side of the...

Can anyone help me to solve the following second order linear 'ODE' for V(x,s,t): \frac{\partial^2 V(x,s,t)}{\partial s^2} = g(s) V(x,s,t) where g(s)=\frac{a^2}{B^4}+\frac{s^2 w^2}{B^2}. Here, a, b and w are (real) constants.

Hi All, I was looking for the general solution of an equation as y(x)'' = f (y), and found the attached document on the web. It presents the solution in a way which I am not sure I understand. I tried to look at the trivila example y'' = - y, solution y = sin (x), but I am struggling in...

Hey everyone, I've been doing some experiments with analog computers to further my knowledge of op-amps (and second order differential equations!) This is more of a mathematical question than an electrical engineering question, so I thought I'd ask it in this section. I'm looking for some...

Terms of "second order" and "fourth order"...what does this MEAN?! I am reading the paper written by Born and Oppenheimer that explains the development of the Born-Oppenheimer approximation. The paper contains the following cryptic (to me) statement: "The nuclear vibrations correspond to terms...

I would very much appreciate if anyone can help me with this problem. I got stuck at the end. I have to find 1.the complementary function, particular integral and the general solution. 2. find complete solution when t=0, q=0, dq/dt=0. -equation...

Hi all, For my thesis I would like to solve the following second order nonlinear PDE for V(x,\sigma,t): \frac{1}{2}\sigma^2\frac{\partial^2 V}{\partial x^2}+\frac{1}{2}B^2\frac{\partial^2 V}{\partial \sigma^2}+a\frac{\partial V}{\partial \sigma}=0, subject to the following boundary...

Homework Statement Solve the initial value problem y" = 2x - y' , y'(0) = 1 , y(0) = 0 I know this is probably a simple problem but I don't have a book for the class yet and the teacher didn't really cover this material in class but we still have homework due on monday so i need to figure...

Hello, I was wondering if I could get some help with a question I have. Homework Statement We are asked to find the first and second order partial derivatives of f(x,y) = x^2 - y^2 - 4x^2/(y - 1)^2 (sorry, I don't know how to write this in latex). I am not really sure how to get started...

Homework Statement Question and part 1 as above. The second part involves solving this equation where L = 8R^2 C. The system is kept in steady state by maintaining V(t) = -Q/C (constant). V(t) is then set to 0 at t=0. It also says "Note that V(t)=0 for t>0 and that appropriate initial...

Top of page 69. I get six second order terms. Two of them cancel. Two are the ones on the right of 3.11. The other two involve KμKμ and KνKν. Why are there no such terms on the right of 3.11? I'm probably just missing something painfully obvious.

In my research, I'm using a modified version of the wave equation: \[ c^2 \left( {\frac{{\partial ^2 p}}{{\partial x^2 }} + \frac{{\partial ^2 p}}{{\partial y^2 }}} \right) = - \tau c^2 \left( {\frac{{\partial ^3 p}}{{\partial t\partial x^2 }} + \frac{{\partial ^3 p}}{{\partial...

How to prove that y''=d2y/dx2 if y=f(x)

Homework Statement find the general solution to the ODE: y''+(1/x)y'=0 Homework Equations The Attempt at a Solution I put this in the following form: y''=-(1/x)y' integrated both sides: y'=-ln(x)y +C I think i made a stupid mistake but i can't figure out what it is. Any help...

Homework Statement if z= f(x) + yg(x), what can you say about zyy explain? Homework Equations The Attempt at a Solution z= f(x,yy) zyy = d/dy (dz/dy) d(partial derivative)

Homework Statement Find the general solution of the following diff. eqn. y''(t) + 4y'(t) + 4y(t) = t^(-2)*e^(-2t) where t>0 Homework Equations General soln - Φgeneral(t) + Φparticular(t) Wronskian - Φ1(t)Φ22'(t) - Φ2(t)Φ1'(t) The Attempt at a Solution I'm solving by...

Homework Statement Find all values of a for which all solutions of y''(x) + (a/x)y'(x) + (5/2)y(x) = 0 tend to zero as x tends 0+ and all values for which all solutions tend to zero as x tends to + Homework Equations The Attempt at a Solution I am not even sure where to being with this...

second order ODE solution for this system?? hello guys, I am wondering if what is the analytical solution for this system? can we solve it as a mass-spring-damper system? thanks for your helps. the rectangular part is removed from the disk. http://img3.imageshack.us/img3/3610/odev.th.jpg

I know there are many ways to identify the spectra but, what are the advantages and disadvantages of using the first and second order lines to identify spectra? Please Help! If u don't want give me answer then suggest me some links. Thanks

Homework Statement The following contour diagram represents the function z = f(x,y) http://img15.imageshack.us/img15/9059/contour.th.jpg (a) Is z an increasing or decreasing function of x? I'd say it's increasing as it goes towards the x-axis the contour lines value goes down (b) Is z...

could anyone help me with solving this second order differential equation? I am a noob on here so not sure how you get the mathplayer stuff on... so the equation is of the form x'' +ax' + bx^n = 0 (x^n means x to the power n, with a and b constants). i tried substituting x'=u to get a first...

Little homework problem that I'm beating myself up over... Solve: xy'' - 2y' + xy = -2\cos x Using the method of Laplace transforms... So I do some jiggling and get to: (1+s^{2})\frac{dF}{ds}+4sF(s) = \frac{2s}{s^{2} + 1} To which I find the following solution: F(s) =...

Hi all, My maths are very rusty and I would need some advice. I have some experimental results obtained in an open channel and got depth-averaged velocity u(y) at different cross-sectional locations y. I tried different models but there is one I don't know how to tackle. The following one...

I'm trying to find a substitution that works for the nonlin diffeq y''+a(y')^2-by=0 Any suggestions?

Hi, I'm having problems solving this equation; y'' -2y' +3y =0 y(0)=-1 , y'(0)=(root 2) -1 I found the auxiliary equation r^2 -2r +3 = 0 and since b^2 -4ac is less than zero this the case where r1 and r2 are complex numbers. This is as far as I get without getting stuck...

Hey guys, I have a question about the Bode diagram of a second order high-pass filter (one with both a capacitance and an inductance). The Bode-diagram of the amplitude looks like this. http://dave.uta.edu/dillon/pspice/images/pst07g.jpg Here, the cutoff frequency is equal to about 10 kHz...

hi, i am facing problem in solving the following differential equation. help me. y''+ayy'+b=0, where y is a function of x, 'a' & 'b' are constants. i have tried substituting y'=u, which implies u'=u*dy/dx, these substitution change the equation to first order but i found no...

1. Homework Statement + relevant equations I have to solve http://home.vs.moe.edu.sg/linl/eqn1.gif sigma, pinfinity, rho, N are constants. To make things easier for us, we are allowed to treat T as a constant. 2. The attempt at a solution Treat T as constant...

Hi In my lecturer's notes he describes the unit tangent to a curve y=Y(X) as (i + Y'(X)j)/[(1+[Y'(X)]^2)^(0.5)] in an introduction to second order PDEs I'm a bit confused by this. Where did it come from? Can anyone explain Thanks

Homework Statement Write a function and solver for the chaotic motion of stars in a galaxy Initial conditions: x at time zero = 0 velocity of x at time zero = 0.3 y at time zero = 0 velocity of y at time zero = 0 Time period 2 to 200 with an interval od 0.02 Homework Equations...

Hello and thanks to all who read this. I'm trying to teach myself applied mathematics, specifically (simple) differential equations. I've been solving them all fine, so far, but now I've come across second order DE's with a squared term, and I can't seem to get the right answer. I'll give...

Homework Statement I am modeling a set of equations for a protein network. It is a feedback loop between 2 proteins. I have gotten the differential equations for this model and plan on doing an extended Kalman Filter to estimate the levels of protein in real time. However, I am having...

Does anyone know how to solve the following Non-linear, second order, differential equation? A*y" + B*(y')^2 = F(t) + C where A, B, & C are constants **please note, in case the above notation isn't clear, the y' term is squared which is what makes it non-linear. Also, F(t) is time...

I would very much appreciate if anyone can help me with this problem; I have approached it from many different angles to no avail. The position x(t) of a particle moving along the x-axis is governed by the differential equation: x'' + kx' + (n^2)x = 0 , and initially x(0) = a, x'(0) = u...

Homework Statement Find the terms up to x^5 in the power series solution of the following equation y''=(1+x^{2})y Homework Equations Power series, sum from 0 to infinity y=\sum a_{n}x^{n} The Attempt at a Solution At first I just differentiated each term separately and...

Homework Statement I've completed this question but I don't think I've got it right. It's from a 2008 June FP1 further maths paper. There is a second part to the question I don't understand which I will post after I know I have got this part right :) Find, in terms of k, the general...

Can someone explain to me why the solution of \frac{d^{2}\Phi (\phi)}{d\phi^{2}} = -m_{l}^{2} is \Phi = e^{im_{l}\phi}?

This is the question word for word: a) Solve the initial value problem: x'' + x = 2cos(\omega t) ; x(0) = 0 ; x'(0) = 0 ; \omega != 1 b) repeat but with \omega = 1 c) use the trigonometric identity: cos(\alpha) - cos(\beta) = -2sin(\frac{\alpha + \beta}{2})sin(\frac{\alpha - \beta}{2})...

Homework Statement A 2-\mu F capacitor is charged to 20 V and then connected across a 6-\mu H inductor forming an LC circuit. (a) Find the initial charge on the capacitor (b) At the time of connection, the initial current is zero. Assuming no resistance, find the amplitude, frequency and...

The Problem You are given: http://img530.imageshack.us/img530/4468/88346476ca9.jpg Where http://img408.imageshack.us/img408/209/53113174nt5.jpg is constant (taken as B). a) Differentiate both sides to produce a second order ODE for y(x) b) Show that it can be written as a first order ODE...