Homogeneous Definition and 382 Threads

Homework Statement Here's my problem - Give the order of linear homogeneous recurrence relations with constant coefficients for: An = 2na(n-1) The Attempt at a Solution I have no idea on how to start this problem - Any help would be greatly appreciated.

Homework Statement I'm told that this is homogenous (x^2-xy)y'+y^2 = 0 2. The attempt at a solution This is going to be very painful for me to type out... (x^2-xy)\frac{dy}{dx} = -y^2 \frac{dy}{dx} = \frac{-y^2}{(x^2-xy)} \frac{dy}{dx} = \frac{-y^2}{(x^2-xy)}...

This is a basic simplification, but I'm going to post this here because it becomes homogeneous, and I know v = \frac{y}{x} but I don't see this simplification, I don't understand how it gets from this... \frac{dy}{dx} = \frac{y-x}{y+x} To THIS: = \frac{v-1}{v+1} (I'm just only showing...

im posed with the question why an equation may be homogeneous with respect to its units but still be incorrect? i can't think of way to explain this can anyone help me out? Thanx

What are their differences? Spatially homogeneous is when there is uniform composition of space Spatially isotropic is when you look anywhere, they look the same Is it the case that one is visit anywhere, it is the same and the other is look anywhere they look the same? They seem...

Hi all, I have been given this question: Find the initial value problem of the homogeneous equation: (x^2 - y^2) y' = xy \ , \ y(1) = 1 Now I know, from my lessons, I have to get it in the form of: \frac{dy}{dx} = f(\frac{y}{x}) I have managed to get close but nothing is...

u_x+u_y+u=e^{x+2y}, y(x,0)=0 I have no idea how to do this. We were only taught how to solve homogeneous first order PDE's.

y''(t)+A^2y(t)=f(t), t>0, y(0)=B, y'(0)=C, A, B, C\in\mathbb{R} e^{iAt} is a particular solution of the homogeneous equation. I can multiply it by some arbitrary function and find another solution of the homogeneous case, but when I try with the f(t) on the RHS, I can't do it. Anyone help?

Hey... So the question is as stated: Show that \frac{1} {M_x + N_y} , where M_x+N_y is not identically zero, is an integrating factor of the homogeneous equation M(x, y)dx+N(x, y)dy=0 of degree n. So I am not too sure where to go with this. I suppose what it's saying is, that I'm...

Higher Order Homogeneous ODE (IVP) [Solved] I am having problems with this IVP: y'''' + y' = 0 y(0) = 5 y'(0) = 2 y''(0) = 4 What I have done so far is: \lambda^3 + \lambda = 0 \lambda(\lambda^2 + 1) = 0 So one roots is \lambda = 0 (though.. can there be a root that...

Solve the initial value problem y''' - 5y'' + 100y' - 500y = 0; y(0) = 0, y'(0) = 10, y''(0) = 250 given that y_1(x) = e^5x is one particular solution of the differential equation. r^3 - 5r^2 + 100r - 500 = 0 r = +/- 10i or 5 complementary solution y_c = e^5x(c1cos10x + c2sin10x) general...

Well actuallly 2 thms. They have to do with homogeneous functions. f(tx1,...,txn) = t^k * f(x1,...,xn). Now how do you show A) d/dx1 f(tx1,...,txn) = t^k-1 * d/dx1 f(x1,...,xn) and B) kt^(k-1)*f(x1,...,xn) = x1*d/dx1 f(tx1,...,xn) + xn*d/dxn f(x1,...,xn) A) In the book They say that...

I have a homework question that I don't really understand what they are asking. The book I am using is terrible so I was hoping someone could shed some light. Question: Give a geometric explanation of why a homogeneous linear system consisting of two equations in three unknowns must...

Can someone give suggestions for this question? Find a basis of solutions for the following second-order homogeneous linear equation for positive x: x^2y``-xy`+y=0

I am having trouble finding the solution to the homogeneous system of linear equations: 2x-2y+z=0 -2x+y+z=0

Hi, I'm having trouble with this ODE: [FONT=Times New Roman]y' + 4xy - y^2 = 4x^2 - 7 [FONT=Times New Roman]=> y' = 4x^2 - 4xy + y^2 - 7 = (2x - y)^2 - 7 => x(dv/dx) + v = (2x-vx)^2 - 7 = x^2(2-v)^2 - 7 I assume this ODE is of the homogeneous type, so...

Well, I'm doing homework (again). I was introduced to homogeneous systems of planes and then asked why there must be at least 1 intersection point. The book gives very little (one sentence) on homogeneous systems so I tried to search around online. My guess is that since all of the...

hi, I have this ODE and I need to obtain the general and the particular solution, this is the ODE Vz''+1/r*Vz'= k where k is a constant thanks

I've seen S^2 written as the quotient SO(3)/SO(2). Can someone run me through how to show this, or point to somewhere that does, as I've only seen it stated?

Q. Determine a homogeneous linear differential equation with constant coefficients having having the following solution: y = C1sin3x + C2cos3x My idea is to differntiate both sides with respect to x and come up with an equation in dy/dx what else? can be done... Is my idea correct.

I have this intial value problem: y''-4y'-5y=0, y(1)=0, y'(1)=2. My AUX equation is r^2-4r-5=0. I factor and get r=5, r=-1 and my equation becomes y(x)=C1e^(5x)+C2e^(-1x) (C1 and C2 are constants). I took the derivative of y(x) and then tried to use my initial value's to solve for C1 and C2. I...

Hi " A function f is called homogeneous of degree n if it satisfies the equation f(tx,ty,tz)=t^n*f(x,y,z) for all t, where n is a positive integer and f has continuous second order partial derivatives". I don't have equation editor so let curly d=D I need help to show that...

Hi, I need some help in finding whether this differential equation is homogeneous or not. 3 (d^2 y / dx^2) + x (dy/dx)^2 = y^2 I know that for example, x^2 dx + xy dy = 0 is homogeneous. But how can I deal with the equation that has (d^2 y / dx^2) and (dy/dx)^2 ? Thanks

Show that the equation is homogeneous with respect to units: I = nAQv I can't prove it, please help

The book only has one example of this and it's really confusing me. (x^2+y^2)dx+(x^2-xy)dy=0 I can see that it's homogeneous of degree 2 They then let y = ux From there they state that dy = udx+xdu (I'm not sure where this is coming from, but can just accept it on faith if I have to)...

A theorem in my textbook is confusing me: For the functions p(t) \ \ \text{and} \ \ q(t) continuous on an open inteval I defined by \alpha < t < \beta : We have differential equation L[y] = 0 where L = (\frac{d^2}{dt^2} + p\frac{d}{dt} + q) The theorem attempts to prove...

(x^2 + y^2)dx + (2xy)dy = 0 I get y = sqrt((kx^5 + x^2)/3) Where k = c2 cubed, and c2 = ln(c) so k = 3ln(c) But, the answer the teacher gave is (x^2)(y^3) - x - ln(y) = c I can't come up with anything remotely close. I know this isn't in a pretty LaTeX form, but I am new and haven't...

Hi, Please bear with me, I've only had the first sort of "pseudo-lecture" in ordinary d.e.'s this past week, and I was doing some reading ahead. It occurred to me that if linear first-order differential equations are those that can be written in the general form: \frac{dy}{dx} + P(x)y =...

Hi, i have a question. Hope you guys can help~ Ques: Give a geometric explanation of why a homogeneous linear system consisting of 2 equations in 3 unknowns must have inifinitely many solutions. What are the possible numbers of solutions for a nonhomogeneous 2 x 3 linear system? Give a...

Is Cosmos Homogeneous, Isotropic ? Is the universe really homogeneous and isotropic? The answer is hidden within the structure of spacetime.

Can someone explain what the homogeneous equation is :redface: and how do you find the 'null vectors' and hence the general solution. Eg. AX = [6] [8] [4] A = [1 2 4] [3 1 2] [0 2 4] X = [2] [0] [1] Find the null vectors of A and general solution.

Hello all! I'm taking a look at Meserve's "Fundamental Concepts of Geometry" for an introduction to the world of geometry. Section 1-7, A geometry of number triples completely confunded me. It introduced homogeneous points, and in my opinion it either a) did a horrible job, or b) did a horrible...