Homogeneous Definition and 382 Threads

Hi all, I would like to know how to determine the number of solutions for a Homogeneous system. Ax = 0 A is a m*n matrix and x is a n*1 vector. There are m equations and n unknowns. I'd like to know how to determine the number of solutions to this system. Thank you in advance.

I have an integral equation of the form y(x) = \int_0^{2\pi} dx'~K(x,x';\omega,\alpha)y(x'), where K(x,x';\omega,\alpha) is a real, non-symmetric, non-separable kernel that depends on the parameters \omega and \alpha, as well as some others that I won't need to vary as much. The kernel is...

Homework Statement Find the solution to :y''+2y'+y=t Homework Equations Suppose y(t)=B1t2+B2t+B3 And I believe, Y(t)=Yh+Yp. That is the solution is equal to the solution to the homogenous equation, plus the particular solution. The Attempt at a Solution First Solve the...

Homework Statement Let n be a positive integer. A function F is called honogeneous of degree n if it satisfies the equation F(tx,ty) = tnF(x,y) for all real t. Suppose f(x,y) has continuous second-order partial derivatives. Show that if F is homogeneous of degree n, then x*F_x + y*F_y =...

Hi, I don't understand why the general solution of 2nd order homogeneous equation is linear? Why is c_1e^(xt)+c_2e^(xt) a linear differential equation? What am I missing here? Any help would be appreciated, I'm struggling a bit understanding the concepts of differential equations...

Homework Statement Find a basis for the solution space of the given homogeneous system. x1 x2 x3 x4 1 2 -1 3 | 0 2 2 -1 6 | 0 1 0 0 3 | 0 The Attempt at a Solution When I reduced to reduced row echelon form i get the following matrix...

Homework Statement See photo Homework Equations The Attempt at a Solution I am learning partial differential and never be taught about homongeneous function. What is this? How to solve the problem?

xcos(y/x)(ydx+xdy) = ysin(y/x)(xdy-ydx) I have started to it by Letting y=vx And then Find it's derivative put their in equation . But the equation afterwards cannot come for finding suitable integral. Kindly help.

Determine which of the following equations are dimensionally homogeneous. Show your work ΔP/Q = 17L(μ)/(w^4) where ΔP is the pressure drop in a channel of triangular cross-section, Q is the volumetric flowrate, L is the channel length, μ is the fluid viscosity, and 2w is the length of one...

[PLAIN]http://www.tempneff.com/jailtime/differential%20equations/HDE.PNG I learned how to solve homogeneous DE's from youtube videos. This presented a problem when during my last test, a question stated that i should show a DE to be homogeneous. The way I learned was different then the rest...

Homework Statement Calculate the general solution of the following DE reducible to a homogeneous one: x+y-2+(x-y+4)y'=0. Homework Equations Not sure. The Attempt at a Solution My idea is first to write the DE into the homogeneous form and then solve it via any method that work...

Homework Statement Find the general solution of the differential equation: (x+y)y'=x-y Homework Equations I want to solve this as a homogeneous differential equation, so our equations are: v=\frac{y}{x}, y=vx, \frac{dy}{dx}=v+x\frac{dv}{dx} The Attempt at a Solution I...

I'm moving on to my next section of work and i come across this example: Consider the homogeneous system x + 2y − z + u + 2v = 0 x + y + 2z − 3u + v = 0 It asks for a basis to be found for the solution space S of this system. And also what is the dimension of S. I know this might be...

Homework Statement The mass of the homogeneous flat plate is 50 kg. Determine the reactions at the supports A and B. I've attached the diagram. The Attempt at a Solution I know I will need to find the center of mass. I don't remember exactly how to do it, but I found the centroid...

Convert the differential equation y"-4y'-12y=0 into a system of two first-order DEs. Write the system as a matrix equation.

Homework Statement Prove that if s and t (both are vectors) satisfy a homogeneous system then so do these vectors. (a) s + t (b) 3s (c) ks + mt | k, s are real Homework Equations The Attempt at a Solution I have no idea where to start.

Homework Statement Find the particular solution to the ODE y"+y=x using power series Homework Equations y=\sum(a_{n}x^{n})The Attempt at a Solution i tried plugging in y=\sum(a_{n}x^{n}) into the original equation and comparing coefficients of x to the first degree, but i am not sure how to...

Before I ask the question, let me remind that desargues theorem states : if two triangles are perspective from one point then they are perspective from one line I'd like to ask whether the order of the steps of the proof I did is correct or not. Since I saw the proof from an article but it...

First, I am a rank novice in cosmology, very rank. However, I do see something that puzzles me. I put some numbers in an Excel spread sheet and I calculate that the early universe was far from homogeneous. I did a few limited searchs and did not find a discussion. Here is what I have...

Homework Statement Let A be an m x n matrix such that the homogeneous system Ax=0 has only the trivial solution. a. Does it follow that every system Ax=b is consistent? b. Does it follow that every consistent system Ax=b has a unique solution? The Attempt at a Solution So if the homogeneous...

Homework Statement Find the general solution to x3y'''-9x2y''+76xy'=0 Homework Equations I'm kind of confused on where to start. I'd suppose you'd throw in y=emx but I'm not positive since there are Xs in there. Once I know what to do with the x terms, I can just find all the roots and that'll...

Solving second order linear homogeneous differential equation! HELP!? Solve the second order linear homogeneous differential equation with constant coefficients by reqriting as a system of two first order linear differential equations. Show that the coefficient matrix is not similar to the...

Assuming knowledge of homogeneous ODEs and nonhomogeneous ODEs that can be made homogeneous (eg, y'-y=x), how does one solve those that cannot be made homogeneous (eg, y'-y=cosx, y''-xy'+y=0, cos(y'')+sin(y')=0)? EDIT: Maybe "made homogeneous" is the wrong way to put it... By being able to be...

I'm stuck on how did the author managed to convert the axis angle to a 4x4 homogenous matrix. Here's the code below. The bolded ones are the one I'm struggling at right now. Before he use the code above. He converted the axis angle to quaternion first which is the one below. I somehow managed...

Homework Statement Show, by means of the Wronskian, that a linear, second-order, homogeneous diffferential equation of the form y''+P(x)y'+Q(x)y=0 cannot have 3 independent solutions. The attempt at a solution I tried by constructing a Wronskian of 3 general solutions expecting the...

Hi. I have to solve this: y''-3y'+2y=e^x, Using the replacement y=\phi y_1 being y_1 a solution of the homogeneous differential equation. I can't do it "traditionally", I have to use this method. So I have to solve that \phi ''y_1+ \phi ' \left[2y_1'+Py_1] \right]=e^x So, this is what I...

Hi there. I had some trouble trying to solve this: y''+y=\cos x +3\sin 2x (1) At first I just found the solution for the homogeneous equation: y_h=e^{\lambda x} \rightarrow \lambda^2+1=0 \rightarrow \lambda_1,\lambda_2=\pm i Then y_h=C_1\cos x+ C_2 \sin x So I've tried to find the particular...

As the title suggests, I do not understand why people set lambda = 1 in proofs of Euler's homogeneous function theorem. Euler's homogeneous function theorem is: i. Definition of homogeneity. Given a differentiable function, f(\vec x), that function is said to be "homogeneous of degree...

I am working on a problem and before I post the remaining questions on it, I want to be sure I calculated the eigenvector correctly. The eigenvalue I used was lambda = 3-4i. \begin{bmatrix} 3-lambda & -4\\ 4 & 3-lambda\end{bmatrix} After substituting, the eigenvector I came up with is V...

3rd order homogeneous Linear ODE matrix transformation---how to write the answer Homework Statement Transform this 3rd order homogeneous linear ODE with constant coefficients using matrix notation. y'''+7y''+6y'+3y=0 Homework Equations The Attempt at a Solution My answer is x'=AX...

Homework Statement Transform this 3rd order homogeneous linear ODE with constant coefficients using matrix notation. y'''+7y''+6y'+3y=0 Homework Equations The Attempt at a Solution I can't find anything useful to start with on this one. I need some with starting this one, I've...

As the title says, what does it mean for an equation to be homogenous?

Homework Statement \dot{x}=2x+5y+1, \dot{y}=-x+3y-4 Homework Equations The Attempt at a Solution Well, if system was: \dot{x}=2x+5y, \dot{y}=-x+3y we let a=2, b=5, c=-1, d=3. Then p = a + d and q =ad - bc and we investigate p^2-4q Don't know what to do when \dot{x}=2x+5y+1...

Homework Statement I have a homework problem that says that any function of the below form is a solution to the homogeneous wave equation. Any function of this form is a solution to the following equation: I would be able to solve it if the function was defined, but I'm not...

Homework Statement xdx+sin\frac{y}{x}(ydx-xdy) = 0 The Attempt at a Solution Well, it's quite easy. But I'm quite confused if this is homogeneous or not, because of the sine function. This is my solution, assuming that this is a homogeneous equation. let x = vy, dx = vdy + ydv; then...

Homework Statement Find the solution of the system x' = 3x + 4y; y' = -2x-3y satisfying x(0) = 2 and y(0) = -1 Thank you Homework Equations The Attempt at a Solution My method involves linear algebra: turn the pair of equations into a single first order vector differential equation of...

what does a homogeneous linear equation in 3 variables represent geometrically ?

Homework Statement Verify that the given vector is the general solution of the corresponding homogeneous system and then solve the nonhomogenous system. Assume that t>0. tx' = |2 -1|x + |1- t^2| |3 -2| |2t | General solution: x = c1| 1|t + c2| 1|t^-1 | 1|...

i am having trouble trying to classify whether or not a differential equation is homogeneous. i know that if it is, f(tx, ty) = tnf(x, y) but i don't really know what this means for example, why is f(x, y) = exy not homogeneous but f(x, y) = ex/y is homogeneous?? does that mean a...

i have the equation x2y' = (y2 - xy) which i changed to (y2 - xy)dx + x2dy = 0 i then tried to solve using the substitution y = xv dy = xdv + vdx so .. (x2v2) dx + x2(xdv + vdx) = 0 (v2 - v) dx + xdv + vdx = 0 v2dx + xdv = 0 (1/x)dx + (1/v2) dv = 0 ln|x| + C - (1/v) = 0 y(x) =...

Homework Statement The problem is setting up the equation, it says that the matrix equation will be made up of four equations for the 2 unknowns. I'm supposed to find for which a's and b's the equation is true, using a linear system and gaussian elimination. Homework Equations A2 + aA + bI2 =...

Homework Statement The equation 2y'' - y' + y2(1 - y) = 0; where y' = dy/dx and y'' = d^2y/dx^2 represents a special case of an equation used as a model for nerve conduction, and describes the shape of a wave of electrical activity transmitted along a nerve fibre. Homework...

i am having trouble finding the general solution for the given homogeneous equation: x2yy' = (2y2 - x2) which i made into x2dy = (2y2 - x2) dx i turned it into the following: (2y2 - x2) dx - x2 dy = 0 then i used substitution of y = xv and got (2(xv)2 - x2 - x2v) dx - x3 dv = 0 then...

Homework Statement homogeneous solution of 235-U and water, contains 10g of 235-U/L of solution, what is the atom density of 235-U and the molecular density of water Homework Equations The Attempt at a Solution first converting 10g/L to 0.01g/cm^3, density of water 1g/cm^3...

I came across of an equality which I have difficulty to understand. If f_n is a rational algebraic homogeneous function of degree n in the differential operators and if g_n is a regular non-differential homogeneous function of the same degree n, following equality takes place [Hobson: The theory...

Homework Statement The problem has to do with diagonalizing a square matrix, but the part I'm stuck on is this: Bx=0, where B is the matrix with rows [000], [0,-4, 0], and [-3, 0, -4]. After performing rref on the augmented matrix Bl0, I get rows [1,0,4/3,0], [0,1,0,0], [0000]. I am...

Homework Statement Suppose you have points of a specific form, say (x, y, 3x + 2y). Show that this set of points is a solution to a homogeneous system of linear equations, hence a subspace. The Attempt at a Solution I'm wondering how one is able to go about this. Here's my try, but I'm not...

Hi, To understand the difference between uniform magnetic fields and field gradients would it help to make comparisons between their effects on different particles? The posts on Stern-Gelach shed some light here. For instance, what effect would a homogeneous and an inhomogeneous magnetic field...

Homework Statement dx/dt=x(1-2y) t(0)=0 x(t(0))=1 dy/dt=-y(1-2x), t(0)=0 y(t(0))=2 inerval of integration= [0,40] Homework Equations The Attempt at a Solution i let x=p(t) so t=(p^-1)(x) dy/dx=(∂y/∂(p^-1))∂(p^-1)/∂x dy/dx=(-y(1-2x))/(x(1-2y)) since this equation is...

While the title may suggest this thread belongs in cosmology, my questions are orientated towards a better understanding of general relativity. Basically, there seems to be an assumption that after the Big Bang, the initial expansion of the universe was slowed by gravity. Many sources appear to...