Homogeneous Definition and 405 Threads

For a Lagrangian L(x^k,\dot{x}^k) which is homogeneous in the \dot{x}^k in the first degree, the usual Hamiltonian vanishes identically. Instead an alternative conjugate momenta is defined as y_j=L\frac{\partial L}{\partial \dot{x}^j} which can then be inverted to give the velocities as a...

So there's this problem in my text that's pretty challenging. I can't seem to work out the answer that is given in the back of the book, and then I found a solution manual online that contains yet another solution. The problem is a the heat equation as follows: PDE: u_{t} = α^2u_{xx} BCs...

Homework Statement Consider the DE (x + y)y′ = x − y. (a) Solve the DE using the homogeneous substitution v = y/x. An implicit solution is acceptable. (b) We can rearrange the DE into the differential form (y − x) dx + (x + y) dy = 0. Is this equation exact? If so, find an implicit...

Hi all I have question in homogeneous . could please check my answer ?

Homework Statement Suppose u, v are two linearly independent solutions to the differential equation u''+p(x)u'+q(x)v=0. If x0,x1 are consecutive zeros of u, then v has a zero on the open interval (x0,x1) Homework Equations The Attempt at a Solution I'm trying to use the...

I've poked back through the past few weeks of threads, and I've only seen two posts (here and here) with very little discussion commenting about the recent Huge-LQG discovery (http://mnras.oxfordjournals.org/content/early/2013/01/07/mnras.sts497.full). I was hoping some cosmologists could...

Homework Statement Use the method for Homogeneous Equations to slove (xy + y^2) dx - x^2 dy = 0 Homework Equations The Attempt at a Solution I attempted to get dx/dy on one side and substitute but could not get farther than this dx/dy = x^2/(xy + y^2)

I quote an unsolved question posted in MHF (November 7th, 2012) by user NumberMunhcer.

In General Relativity (GR), we have the _geodesic deviation equation_ (GDE) $$\tag{1}\frac{D^2\xi^{\alpha}}{d\tau^2}=R^{\alpha}_{\beta\gamma\delta}\frac{dx^{\beta}}{d\tau}\xi^{\gamma}\frac{dx^{\delta}}{d\tau}, $$ see e.g...

Hi. If I have a homogeneous ODE with constant coefficient system in the form of 2x2 matrix: X'=A X, A is a 2x2 matrix. How do I solve this using wolfram or matlab?

$R(r) = A_m\mathcal{J}_m(kr) + B_m\mathcal{Y}_m(kr)$ $$ \begin{pmatrix} \mathcal{J}_m(ka) & \mathcal{Y}_m(ka)\\ \mathcal{J}_m(kb) & \mathcal{Y}_m(kb) \end{pmatrix} \begin{pmatrix} A_{m}\\ B_{m} \end{pmatrix} = \begin{pmatrix} 0\\ 0 \end{pmatrix} $$ In order for our system to have a non-trivial...

Homework Statement I'm trying to understand the simplification of the general solution for homogeneous linear ODE with complex roots. Homework Equations In my notes, i have the homogeneous solution given as: y_h (t)= C_1 e^{(-1+i)t}+C_2e^{(-1-i)t} And the simplified solution is given as: y_h...

Differential equations Homogeneous Linear Equations case 1 +example - YouTube There are more on my channel and will be posting more daily.

Homework Statement Let G be a compact connected Lie group define the loop group and the based loop group as LG = \{ \gamma \in C^\infty(S^1,G) \}, \Omega G = \{ \gamma \in LG : \gamma(e_{S^1}) = e_G \} (choose whatever identification of the circle S^1 you like ). Show that \Omega G is a...

Homework Statement Ok I have this general homogeneous function, which is a C^1 function: f(tx,ty)=t^k f(x,y) And then I have to show that this function satisfies this Euler equation: x\frac{\partial f}{\partial x}(x,y)+y\frac{\partial f}{\partial y}(x,y)=k\cdot f(x,y) Homework...

Four days ago on mathhelpforum.com the user ssh [I don’t know if he the same as in MHB…] has proposed the following second order complete linear ODE… $\displaystyle y^{\ ''} – \frac{2+x}{x}\ y^{\ ’}\ + \frac{2+x}{x^{2}}\ y = x\ e^{x}$ (1) … and till now no satisfactory solution has been...

How to solve \( (x+1) y'' - (2x+5) y' + 2y = (x+1) e^x\) can we assume \(y_1 = (Ax+B) e^x \), then \(y_2= vy_1​\) Is this right? then solve for A and B Finally \( y = c_1 y_1 + c_2 y_2\)

The Cauchy homogeneous linear differential equation is given by x^{n}\frac{d^{n}y}{dx^{n}} +k_{1} x^{n-1}\frac{d^{n-1}y}{dx^{n-1}} +...+k_{n}y=X where X is a function of x and k_{1},k_{2}...,k_{n} are constants. I thought for this equation to be homogeneous the right side should be 0. (i.e.)...

Actually I can't find if a differential equation is homogeneous or not I thought homogeneous is given by dy/dx= f(x,y)/ g(x,y) but it doesn't look like that For eg: dy/dx= (y+x-1)/(y-x+2) is not homogeneous at all though f(x,y)=y+x-1 and g(x,y)=y-x+2 How can you tell...

To Solve y’’ – 2 y’ – 3y = 64 e-x x ---------------(1) Using the method of undetermined coefficients : The roots of the homogeneous equation are 3 and -1, so the complimentary solution is y = c1 e3x + c2 e-x Then the guess for the particular solution of (1) is e-x x (Ax + B)...

Hello, I have temperature and emissivity data values for different land types (i.e. rock, vegetation etc.) of an area in form of image pixels. Because there are different land types, they show different temperatures. I want to know the temperature of these pixels as if they were of the same...

we say the universe around us is isotropic and homogeneous. it means that all direction and points are the same for some special class of reference. if this is true why we say in large scale universe is isotropic and homogeneous? it seems that the space, itself, to be isotropy and...

Homework Statement y"-2y'+5=0, y(∏/2)=0, y'(∏/2)=2 find general solution of this diff eq Homework Equations The Attempt at a Solution i have followed all of the steps for this, rather easy 2nd order diff eq, but i my solution differs from the books solution. steps...

How is it possible that an equation shown to be homogeneous with respect to its unit may still be incorrect .

Homework Statement Find the values of α for which all the solutions of y''-(2α-1)y'+α(α-1)y=0 (a) tend to zero and (b) are ilimited, when t->∞. Homework Equations y''-(2α-1)y'+α(α-1)y=0 => (t)=Ae^{αt}+Be^{(α-1)t} The Attempt at a Solution I found that the general solution to the...

I'm reviewing Projective Geometry. This is an exercise in 2D homogeneous points and lines. It is not a homework assignment - I'm way too old for that. Given two points p1 (X1,Y1,W1) and p2 (X2,Y2,W2) find the equation of the line that passes through them (aX+bY+cW=0). (See...

Homework Statement y' = \frac{2xy + y^{2} + 1}{y(2+3y)} Homework Equations The Attempt at a Solution First I tried making a substitution in the case that it is homogeneous, but it didn't make the equation separable. It's not linear, it's not exact, and not separable. Does it...

Homework Statement Calculate the moments of Inertia I_{1}, I_{2}, I_{3} for a homogenous sphere Homework Equations I_{jk}=\intx^{2}_{l}\delta_{ik}-x_{i}x_{k}dV The Attempt at a Solution For I_{x} i set up the equation using the above equation in cartesian coordinates and then i...

Could someone explain them?

Could someone explain the following theorem to me: Given a homogeneous system of n linear equations in m unknowns if m>n (i.e. there are more unknowns than equations) there will be infinitely many solutions to the system.

Homework Statement Find a solution (Z2) of: z'' + 2z - 6(tanh(t))2z = 0 that is linearly independent of Z1 = sech2Homework Equations The Attempt at a Solution reduction of order gives you v''(t)(Z1(t))+v'(t)(2 * Z1'(t)) + v(t)(Z1''(t)+p(t)Z1'(t)) = 0 however the third term on the LHS can be...

Hi everyone, It's not a real homework problem, but something I am trying to do that I haven't found in the literature. I am still stating the problem as if it was a homework Homework Statement Consider a FRW Universe. That is, ℝ x M, where M is a maximally symmetric 3-manifold, with a RW...

Homework Statement dy/dx = (6x^(2)+xy+6y^(2))/(x^2) Homework Equations v = y/x y' = v + xv' The Attempt at a Solution y' = tan(6ln(abs(x))-C)/x ===> apparently not correct

Can anyone explain this to me? If we have an infinite amount of balls arranged in a kind of cubic matrix, in an infinite and static space...how the heck would that collapse on itself due to gravity? Thanks folks

Given a homogeneous linear least squares problem: A^{T}y=0 What is the difference between minimizing y^{T}AA^{T}y (the least square error) and: y^{T}AA^{+}y=y^{T}A(A^{T}A)^{-1}A^{T}y ? Thanks.

Homework Statement I uploaded the problem statement please see attachment for original problem. The problem number is 4. Homework Equations The Attempt at a Solution For clarity I uploaded what I have done please see the attachment with my work on it. I am not sure if I am doing...

Homework Statement Find the set of functions from (-1,1)→ℝ which are solutions of: (x^{2}-1)\frac{d^{2}y}{dx^{2}}+x\frac{dy}{dx}-4y = 0 Homework Equations The Attempt at a Solution There is a hint which says to use the change of variable: x=cos(θ) doing this I get...

how am i going to determine if a higher order differential equation is homogenous? example, d4y/dx4+d2y/dx2=y d3y/dx3-d2y/dx2=0

Homework Statement Find the set of functions from (-1,1)→ℝ which are solutions of: (x^{2}-1)y''+xy'-4y = 0 Homework Equations The Attempt at a Solution OK, I'm not really sure how to go about solving this equation, I have only previously attempted problems where the functions in...

Homework Statement The problem is to solve: y''-2y'+5y = e^{x}(cos^{2}(x)+x^{2}) Homework Equations The Attempt at a Solution I (think I) have solved the associated homogeneous equation: y''-2y'+5y = 0 giving the solution as: y_{h} = e^{x}(C_{1}cos(2x)+C_{2}sin(2x))...

I feel that it may be redundant to rewrite the whole problem. I just need to know how the book got from point to point b. The book says that e^{-3x} \frac{dy}{dx} - 3y (e^{-3x}) = 0 is the same as \frac{d}{dx}(e^{-3x}y) = 0 How? I tried dividing and multiplying by some variables to get the...

I have a question; help is welcome. Let sn be a linear, non-homogeneous recurrence sequence, and let hn be a corresponding homogeneous sequence (with initial values to be determined). As it turns out, the offset between the two (sn - hn) is given by the steady state value of sn, if the...

hello every body. I have a high school problem a straight horizontal wire is falling freely in a homogeneous horizontal magnetic field, perpendicular to the wire and i want to find the inductive voltage. I said E= Blv=Blgt But I can also say E=ΔΦ/Δt=BΔΑ/Δt=Βl1/2gt [t][2]/Δt=1/2Blgt why...

Heat Equation (Non Homogeneous BCs) - Difficult Laplace Transform... help! ;) Hi I'm trying to model the temperature profile of an inertia friction welding during and after welding. I have the welding outputs and have come up with a net heat flow wrt time during the process. I now want to...

Homework Statement I have this statement: If M(x,y)dx+N(x,y)dy=0 is a homogeneous DE, then μ(x,y)=\frac{1}{xM+yN} is its integrating factor. The problem is, how do we derive this integrating factor? Homework Equations For homogeneous DE, we have f(kx,ky)=k^n*f(x,y) We also have...

Homework Statement I need to find the general solution of the system [3 5] [-1 -2] Homework Equations so to get the eigenvalues, det(A - λI) The Attempt at a Solution determinant is (3-λ)(-2-λ) + 5 which would be λ2 - λ - 1 so by the quadratic equation the eigenvalues are...

My doubt is that is dimension of a 2nd order homogeneous equation of form y''+p(x)y'+q(x)=0 always 2 ? or dimension is 2 only when p(x),q(x) are contionuos on a given interval I..??

I semi understand the reduction of order method, and i understand the general solution for a 2nd order with repeated roots. however, i can't seem to form up the correct thing to solve this question, and research again proves futile. Any assistance will be appreciated. Use the method of...

I was given a question and i am really unsure how to go about solving it. it appears to be solveable using the characteristic equation and whatnot, however i have my coeffecients in terms of the independent variable. so i am confused. the question initially asked to compute the wronskian, and it...

do you have a idea about it?can you help me http://img17.imageshack.us/img17/1156/18176658.png