Variation Definition and 575 Threads

Hey ya'll! This is the equation under discussion: y'' - 2y' - 3y = x + 2 I'm asked to use the method of variation of parameters to determine a solution for this differential equation, but I reach a point where my the equations just look too ridiculous to continue. The point I have in...

i m little confusd in (finding the shortest distance b/w two points is a straight line in three dimensions)i have solved it but nothing found any accurate result [ds][/2]=[dx][/2]+[dy][/2]+[dz][/2] is the distance in 3-dimension b/w 2 points then how we can start and how we can take...

Homework Statement what is general solution of 2y'' - 3y' + y = ((t^2) + 1)e^tHomework Equations my particular solution is: (e^t) ((2/3)(t^3) + 6t -4)) prof particular solution is: ((1/3)(t^3)(e^t)) - 2(t^3)(e^t) + 9(te^t) The Attempt at a Solution here is how i solved , i hope this is ok to...

Total variation is defined by \Delta f=\delta f+\Delta x For example f(x,y)=yx, y=y(x) \Delta f=x\delta y+\Delta x How is defined \Delta x. Is that rate of change of x, while y is constant?

As you will see this is my first post so I apologize if I have chosen the wrong sub-forum. My academic training (maths) was many years ago and it now seems to me that for the last 30 or so years my brain has been in a kind of intellectual limbo from which it is only now beginning to emerge, so...

Hello guys, hope everything is going well. Anyways, I was thinking recently about the forumla for finding the distance an object has traveled with a constant acceleration using the formula D = V°(t) + 1/2 (A)(t)2 So basically when thinking about this formula, I like to think about an...

Homework Statement Given, β=100, Is = 6E-16 See attachment. a) Find min value of Rb such that the BJT is in active region b) For the Rb found, what is the base-collector voltage if β=200 Homework Equations The Attempt at a Solution Assuming, VCE min for active region operation...

Homework Statement A sample of 1.00 mol of an ideal diatomic gas, initially at pressure P and volume V, expands until it has a pressure of 2P and a volume of 2V. What's the entropy change in the gas on this process? Homework Equations 2nd Maxwell relation: 4th Maxwell relation...

If f has minimum, than \delta f=0, \delta^2 f>0 or \delta f>0?

Homework Statement The goal of the question I'm being asked is to show that the covariant derivatives, D_{\mu}, "integrate by parts" in the same manner that the ordinary partial derivatives, \partial_{\mu} do. More precisely, the covariant derivatives act on the complex scalar field...

Hi all, I'm reading Sean Carroll's Space Time and Geometry and haven't figure out how equation 4.64 is derived, where he is in the process of deriving Einstein's equation from Hilbert action. Given there is a variation of the metric, g_{\mu\nu} \rightarrow g_{\mu\nu} + \delta g_{\mu\nu}, The...

If in the twin paradox instead of the twin traveling to the distant star let's say he stays and the Earth along with that star moves (imagining a rod joining Earth and star moves) and the star reaching this twin goes back at the same speed(along with earth) now i guess the twin whos stationary...

Hello, I want to calculate the total variation \left \| f \right \|_{V(\Omega)} with \Omega=(-1,1) and f(x)=\mathrm{sgn}(x). The total variation of a function is defined as follows: \left \| f \right \|_{V(\Omega)} :=\sup\left \{ \int_\Omega f\ \mathrm{div} (v)\ dx \ | \ v \in...

I'm not sure if this is the right place to post this, but it seems to be the best fit. Homework Statement I'm trying to write a lab report about how resistance varies with temperature. I used liquid nitrogen to cool a copper coil and a semiconductor(thermistor) from room temperature to...

Frequency distribution not determined by the temporal variation of the pulse? In his book Modern Optical Spectroscopy, William Parson says Light from an incoherent source such as a xenon flash lamp contains a distribution of frequencies that are unrelated to the length of the pulse...

Hi, In the usual Gambler's ruin problem one calculates the probability of reaching some target balance N before going broke, given that one starts with holdings of 'h', and given that on each bet he either increases or decreases his balance by +/-1. See...

Homework Statement By what factor is the total pressure greater at a depth of 850 m of sea water than at the surface where the pressure is one atmosphere? (water density = 1000 kg/m3, one atmosphere pressure = 1.01 x 105 Pascals (N/m2), g = 9.8 m/s2 ) Homework Equations P=P(initial)+ρgh...

Problem - Given the following table x y 15 50 26 46 32 44 48 43 57 40 a) Find the sample mean b) Find the covarince matrix c) Perform principal component analysis and find a size index which explains the greatest variation. My attempt a) n = 5 xbar = Sum(x)/n = 35.6 ybar =...

Hi Imagine there is a closed-loop pipeline which we are pumping pure water. Reasonably, we expect the pressure-drop to increase towards the end, due to friction and minor losses. My question, however, is about the velocity. When you half the length of the loop, at the same pump power...

Homework Statement Solve using variation of parameters y''' - 2y'' - y' + 2y = exp(4t) Homework Equations Solve using variation of parameters The Attempt at a Solution I got the homogenous solutions to be 1, -1, and 2. So, y = Aexp(t) + Bexp(-t) + Cexp(2t) + g(t) I got...

The question I'm trying to solve is: y" - 6y' + 9y = \frac{exp(3x)}{(1+x)} I formulated the Gen solution which are: y1(x) = exp(3x) and y2(x) = xexp(3x) I've then calculated the wronskian to get: exp(6x) I then went onto to use the variation of parameters formula, which is where...

I just realized you can use variation of parameters (VOP) to solve for homogeneous 2nd order equations. I see it takes much longer to do so. But I was wondering why, if you use VOP, the u and v functions are 0. Is this because the coefficients of the homogeneous equation are constant, or...

Homework Statement "Vary the following actions and write down the Euler-Lagrange equations of motion." Homework Equations S =\int dt q The Attempt at a Solution Someone said there is a weird trick required to solve this but he couldn't remember. If you just vary normally you get \delta...

Find the complementary solution of y^\left(4\right) + 2y'' + y = sint Homogeneous Form would be y^\left(4\right) + 2y'' + y = 0 r^4 + 2r^2 + r = 0 \rightarrow r(r^3 + 2r + 1) = 0 This is where I'm stuck. Once I find y_c(t) I should be able to finish the problem, but I'm having trouble at this...

Hi everyone, i have a question abuot how my professor is using the pressure variation equation and I would really appreciate help with it! Homework Statement How high can you suck water up a strw? The pressure in the lungs can be reduced to about 10 kPa below atmospheric pressure 2...

Does youngs modulus of elasticity depend upon temperature?

Homework Statement I must solve (1-x)y''+xy'-y=(1-x)^2 knowing that y=x is a solution if the right hand side is 0. I must use this fact in order to obtain the general solution to the DE Homework Equations Variation of parameters? The Attempt at a Solution I'm looking at...

Homework Statement The most commonly used algorithm for computing \sqrt{a} is the recursion xn+1 = 1/2 (xn + a/xn), easily derived by means of Newton's method. Assume that we have available to us a very simple processor which only supports addition, subtraction, multiplication, and halving (a...

Homework Statement I am reading Shrödinger's first paper and have some problems understanding it. This is the first step I don't follow. The below is for Keplerian motion and comes from the Hamilton-Jacobi equation. This is what is said: Our variation problem then reads...

I read the following in Fowles & Cassiday's Mechanics: "The correct motion that a body takes through space is that which minimizes the time integral of the difference between the kinetic and potential energies" or \deltaJ = ∫ L dt = 0...

I've picked up a bit more since my last problem. I need to solve the following DE: x^{2}\frac{dy}{dx}+x(x+2)y=e^{x} I decided to use variation of parameters, so I re-arranged it like so: \frac{dy}{dx}=\frac{e^{x}}{x^{2}}-(1+\frac{2}{x})y Then solved the homogenous DE...

Can somebody clarify how the formula for variation of the auxilliary worldsheet metric is obtained due to reparametrization of the worldsheet in string theory??

I need to find a solution to the following problem: (x^{2}-1)\frac{dy}{dx}+2y=(x+1)^{2} y(0)=0 I decided to try using variation of parameters. My teacher was unable to show any examples, and I'm having issues understanding the textbook. From what I see I need to get it onto this form...

Homework Statement Pascal's law states that " The pressure in a fluid at rest is the same at all points if they are at the same height" Also we know " Pressure increases with depth" I get confused. When pressure increases with distance, how pressure is same at all points. Homework...

[b]1. Homework Statement [/ The value of acceleration due to gravity (g) at an altitude (h) is gh = g (1 - 2h/R). Similarly the value of g at a depth (d) is gd = g(1 - d/R), where R is the radius of the earth. Homework Equations In both the cases, my book says the value of g decreases...

Homework Statement Using the variation of parameters method, find the general solution of x^{2}y" - 4xy' + 6y= x^{4}sin(x) Homework Equations y_{P}=v_{1}(x)y_{1}(x) + v_{2}(x)y_{2}(x) v_{1}(x)'y_{1}(x) + v_{2}'(x)y_{2}(x)=0 v_{1}(x)'y_{1}(x)' + v_{2}'(x)y_{2}(x)'=x^{4}sin(x)...

Given an action: S = \int L(q,\dot{q},t) \,dt The variation is: \delta S = \int \left(\frac{\partial L}{\partial q}\delta q+\frac{\partial L}{\partial \dot{q}}\delta\dot{q}\right)\,dt I'm guessing this is some type of chain rule, but I haven't been able to derive it... how is it...

Homework Statement Find a particular solution for these second order differential equations. Homework Equations 1) y''+9y=tan3t 2) y''+y=tan^2t The Attempt at a Solution I want to find a fundamental solutions y1 and y2 because I want to find a particular solution like this...

Homework Statement Solve for general solution with variation of parameter y'''(x) - y'(x) = x The Attempt at a Solution I initially looked at y'''(x) - y'(x) = x only and I foudn my answer to be y(x) = C_1e^{x} + C_2e^{-x} + 1 - x Now i looked through my book and it says it works for...

Homework Statement The Schrodinger equation (in atomic units) of an electron moving in one dimension under the influence of the potential -delta(x) [dirac delta function] is: (-1/2.d2/dx2-delta(x)).psi=E.psi use the variation method with the trial function psi'=Ne-a.x2 to show that...

If a 1kg object is moving at 3m/s in a positive direction, and a 12N force is applied in the negative direction, what is the velocity immediately after 2s? I'm fairly sure this will be a variation of relevant momentum equations, and/or mixed with kinematics, yet I'm not seeing the correct...

My first post, yay i already like the atmosphere here :P anyway... Using the formula F = kQq/R2 sketch graphs between a. F and Q (k,q, and R are constant) b. F and R (Q,q and k are constant) c. Q and R (k,q and F are constant) I think i did it correctly but I'm not quite sure...

I'm currently working through General Relativity and I'm wondering how you would express the variation of a general metric tensor, or similarly, how you would write the total differential of a metric tensor (analogous to how you would write the total derivative for a function)? Also, on a...

Hi. During daytime sea water having poor solar reflectivity remains warmer than the air. But at times, water has also been found to be colder than air, with the difference being 5-10 degrees C. Can anyone please justify how could that be possible?

Work done by a gas = PV But when we derive specific heat of the gas at constant volume, even though the pressure changes we take work W=0. Or in the case where both pressure and volume are changing and we want to find work done we take the integral of d(PV) where we replace P with nkT/V. Also...

Am I right in thinking that the statement "f:[a,b]-->R is of bounded variation" is equivalent to the statements "f:[a,b]-->R has bounded range" and "f;[a,b]-->R is a bounded function".

Given t^2 y'' -t(t+2)y' = (t+2)y= 2t^3 and y1= t, y2= te^t Find the particular solution- I ve worked the problem to [ -2t^2 -2t] by: -t * Integral [ 2t* te^t/ t^2e^t] + te^t * Integral [ 2t^2/ t^2e^t] whereas the book states that it is simply -2t^2. Can you guys tell me where I made...

So I'm doing some practice problems to prepare for a test on Friday and I'm just curious about this problem:: y'' + 3y' + 2y = 4e^(x) in factoring using characteristics: (r+2)(r+1) = 0 r = -2,-1 so Yc = C1*e^(-2x) + C2*e^(x) y1= e^(-2x) y2= e^(-x) (skipping some algebra)..I...

Hi All, is there anybody to give me some help on how I can calculate the Euler Lagrangian equation associated with variation of a given functional? I am new with these concepts and have no clue about the procedure. thanks a lot

Hello! I have a question? Does anyone know if scientists have tried to run the electrons through the double slit, record the particles that go through each slit, and before looking at the results, looking at the pattern on the screen. And THEN doing the EXACT OPPOSITE of what the screen...