Homogeneous Definition and 382 Threads

Homework Statement Given a differential equation. ie. y'' +y' + 1 =0 (THIS IS NOT THE PROBLEM THAT I AM SOLVING) Homework Equations No equations The Attempt at a Solution The equation above is not what I'm working with, but an example of a differential equation problem that I was...

Hi guys, I've been out of the loop with differentials for some time, and was hoping to get some direction with these.. Given that: (x^2)y" + 2x(x-1)y' - 2(x-1)y = 0 A) Explain why the general theory doesn't guarantee a unique soln to the equation satisfying the initial conditions y(0)...

Homework Statement Prove that in the homogeneous deformation, particles which after the deformation lie on the surface of a shere of radius b originally lay on the surface of an ellipsoid. Homework Equations homogeneous deformations are motions of the form: xi=ci + AiRXR where ci...

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 =...

Can someone explain to to me how to find the general solution of the fourth order ODE y''''-y''=0 Right now I have y(x)=a+b*x+c*e^-x+d*e^x where a,b,c and d are constants. Not sure if this is correct just wanted to double check.

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...

Homework Statement y2dx -x(2x+3y)dy =0 I have to recognize the equation and solve it Homework Equations The Attempt at a Solution I did y2dx - (2x2+ 3yx) dy=0 which is a homogeneous now after I substitude x=uy dx=udy + ydu I stuck here after the substitution...

Hey guys, I've been stuck on this problem for a good hour... I have no idea how to finish it up. Homework Statement Solve: dy/dx = 4y-3x / (2x-y) Use homogeneous equations method. Homework Equations Answer : |y - x| = c|y + 3x|5 (also y = -3x)The Attempt at a Solution dy/dx = 4y-3x / (2x-y)...

Homework Statement So the problem goes like this: dy/dx = ( x^2 + xy + y^2 ) / x^2 a) Show that it is a homogeneous equation. b) Let v = y/x and express the eqn in x and v c) Solve for y Homework Equations (Included) The Attempt at a Solution a) dy/dx = ( x^2 + xy + y^2 ) / x^2 * [(1/xy)...

I read that the 'Homogeneous Differential Equation' is one which has form \frac{\mathrm{d}y}{\mathrm{d}x} = f\left(\frac{y}{x}\right) but I came across one example which was \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{x+y}{x+5y} and said that is 'Homogeneous Differential Equation' Too which has 'x'...

Homework Statement Please help me with this, I would really appreciate it: Using the fact that y1 = x-1/2 cos x is a solution of the associated homogeneous problem, obtain the general solution of x2 y'' + x y' + (x2 - 1/4)y = x3/2 The Attempt at a Solution Well the first thing i...

What's the difference between Isotropic and Homogeneous material? Thanks for your help

Homework Statement Find the general solution of \frac{dy}{dt} + 2y = 3t^2 + 2t -1 Homework Equations The Attempt at a Solution So just worrying about the right side y_p = at^2 + bt + c so \frac{dy_p}{dt} + y_p = 2at + b +at^2 + bt + c = 3t^2+2t - 1 at^2 = 3t^2...

Homework Statement Can y = sin(t^2) be a solution on an interval containing t = 0 of an equation y'' + p(t)y' + q(t)y = 0 with continuous coefficients? Homework Equations The Attempt at a Solution y = sin(t^2) y' = 2tcos(t^2) y'' = 2cos(t^2) - 4t^2sin(t^2) 2cos(t^2) -...

First Order Linear Non-Homogeneous Equation Homework Statement I need to solve for e(t) Homework Equations Do I use Laplace Transform for the last integral? The Attempt at a Solution \begin{subequations} \begin{eqnarray} \nonumber \dot{\hat{{\cal E}}}(t) &=& -\kappa...

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...

I recently read an article about whether the http://dailyphysics.com/" and/or isotropic. (the story is at the top - sorry I couldn't get the link to the permanent article to work here) “gargantuan ripples in the density of matter across the universe, known as baryon acoustic oscillations” is...

Differential Equation w/ Homogeneous Coefficients - y=ux substitution I am teaching myself, this problem is from ODEs by Tenenbaum and Pollard. This is not homework for a class. Homework Statement (x+y){dx} - (x-y){dy} = 0 Homework Equations y=ux, {dy} = u{dx} + x{du} The...

Hello everyone! I'm trying to solve 2 questions for my assignment on homogeneous ODEs I can solve ODE's with variation of parameters and with the method of undetermined coefficients, but these 2 methods seem useless when the coefficients are not constant : (x^2)y" - 2xy' -54y = 0 and...

Homework Statement Let A * x= 0 be a homogeneous system of n linear equations in n unknowns, that has only the trivial solution. Show that if k is any postive integer, than the system A^k * X = 0 also has only the trivial solution. The Attempt at a Solution I'm so lost please help...

Homework Statement Determine the x-coordinate of the mass center of the homogeneous hemisphere with the smaller hemispherical portion removed? I know what the answer should be it's Xcm = 45/112 R Homework Equations The center of mass R of a system of particles is defined as the average...

Homework Statement "Solve the following ODE's:" "3u+(u+x)u'=0" This is our first weeks homework and he went this through this so quickly in class. Homework Equations None. x and u are both variables. The Attempt at a Solution I know it is homogeneous and non linear. I tried v-substitution...

Homework Statement The following DEs are homogeneous and can be solved using a substitution y=ux or v=xy. I can solve them, I'm just don't see how they are homogeneous. How is it that with there being an exponent (y/x) that this is homogeneous. I don't see how I could pull out t\alpha...

The concept of invariance of an object, property, etc... should always expresses with respect to something else: time-invariant means static. space-invariant means homogeneous. direction invariant means isotropic. "Something" can have just one of those types of invariance, all three of...

this is the given equation y'=(4y-3x)/(2x-y) and here is all the work I've done so far: (4v-3)/(2-v)=v+x*dv/dx i moved v over and came up with this (-3+2v+v^2)/(2-v)=x*dv/dx did a flip (2-v)/(-3+2v+v^2)dv=dx/x by partial fractions I got a=-3/2 and b=1/2 so...

Homework Statement Given, (y+2)dx + y(x+4)dy = 0, y(-3) = -1Homework Equations v=y/xThe Attempt at a Solution I've been REALLY struggling with homogeneous equations for some reason...I just don't understand them all. so far I've tried two things. (1)dx -(y)dy ----- ------- (x+4)...

Hi everyone. I am really confused at the moment learning about Second Order homogeneous linear differential equations. I lay out the background of what I would like to understand. So I understand the actual maths that goes into the diff's, but I do not understand why it should be so, given the...

Hey all, i think I'm doing most of this right, but I'm missing a coefficient somewhere when integrating or something... Homework Statement Substitute v=y/x into the following differential equation to show that it is homogeneous, and then solve the differential equation...

I have a question: If the vectors of v & u are solutions of the nonhomogeneous linear system Ax=b, then ru+sv is a solution of the nonhomogeneous system for any real values of r and s. is this statement true? is this statement true for homogeneous systems too?

xy'-y =sqrt((x^2)+y(^2)) so by method of homogeneous equations I get arcsinh(y/x) = ln|x|+c but don't know what to do from there. the book suggests using sinhx = 1/2 (e^x - e^-x) but I don't know how to incorporate this. The answer should be y= (1/2) * (cx^2 - 1/c). How do you get this? This is...

Hi guys Please take a look at this familiar picture: http://www.astr.ua.edu/keel/galaxies/wmap_map.jpg Does this imply that the universe was not perfectly homogeneous or that it was anisotropic at the time of photon-decoupling? Since the CMB-fluctuations are because of the different...

I just finished a final in my differential equations class. One of the problems had me solve a second order homogeneous differential equation using series. I boiled it down to this recursion relation: a_{n+2}=\frac{(n+3)a_{n}}{2(n+2)(n+1)} I found that the even coefficients work out...

Hey; not much of a homework question, but something i was wanting to find out. Im still a first year undergraduate and just started on differential equations. We have just finished going over homogeneous 2nd order ODE's of the form: ay'' + by' + cy = 0 My texbook briefly outlines the...

hey I am having a little trouble with this topic. Here are the questions I was set. a) Find the general solution of d^2y/dt^2 - 2(dy/dt) + y = 0. Verify your answer. b) Solve the initial value problem y'' + 4y' + 5y = 0; y(0)= -3, y'(0) = 0 c) Find a DE that has the given functions as...

,so in class we're covering second-order D.E.s... How exactly was it determined/derived that all solutions to homogeneous 2nd-order linear differential equations with constant coefficients (ay'' + by' + cy =0, where a,b,c are real constants) are of the form y=ert. Not asking for anyone to...

Homework Statement Show that id y = x(t) is a solution of the diff. eqn. y'' + p(t)y' + q(t)y = g(t), where g(t) is not always zero, then y = c*x(t), where c is any constant other than 1, is not a solution. Homework Equations Can someone help me get started? Also, since g(t) is not...

1. solve the following recurrence relation for a[SIZE="1"]n 2. (n+2)a[SIZE="1"]n+1= 2(n+1)a[SIZE="1"]n+2^{n}, n>=0, a[SIZE="1"]0=1 I shifted the index, multiplied through by the 2^{n} term and then subtracted the resulting equation from the original equation to get rid of the 2^{n}...

Homework Statement let x^{(1)} = \left( \begin{array}{ccc}1\\1\\1\end{array} \right) , x^{(2)} = \left( \begin{array}{ccc}1\\t\\t^2\end{array} \right) , x^{(3)} = \left( \begin{array}{ccc}1\\t\\t^3\end{array} \right) a) Find the Wronskian W(x^{(1)}, x^{(2)}, x^{(3)}) b) You are...

I have to show that the hamiltonian for a homogeneous system can be simplified in scaled coordinates. The first two terms I can convert to scaled coordinates <T>+<V> whereas I have some trouble for the last term -½* \int d³r d³r' \frac{n²}{|r-r'|} where n is the density. The scaled...

Homework Statement Classify each of the following as a pure substance, solution, or heterogeneous mixture: a) blood b) dry ice c) krypton gas d) a rusty nail e) table salt f) glass of lemonade Justify your answers. Homework Equations No equations obviously...The Attempt at a Solution Here's...

I've managed to derive from Maxwell's equations the homogeneous electromagnetic wave equation with respect to the magnetic field. (The one that goes Del Squared of H minus (The second order partial derivative of B multiplied by the recipricol of C squared all equal to zero) Hopefully that...

Homework Statement A homogeneous ladder having a length of 6m and a mass of 35kg is positioned. The lower base of the ladder has an angle of 60 degrees with the ground and the coefficient of friction between former and the latter is 0.3. Define the maximum height a human can reach, which...

I need some help here... I've got the following assignment to do Prove that if M>N then any system of N homogeneous equations in M unknowns has many solutions. I am a bit stuck with this one. I thought about creating a MxN Matrix and to display the determinant with 1's. and then say...

I've been confused for a little while as my teacher in dif. eq.'s taught us about homogeneous equations, where you can call an eq. homogeneous if all terms are of the same degree. But then, when seeing linear dif. equations we were taught that an homogeneous eq. is one with certain form and...

I am trying to solve the diff. equation - a\frac{d^{2}x}{dr^{2}} + (br + c/r)\frac{dx}{dr} + dx = 0 I got it while solving a variant of damped harmonic oscillation. Any hints (Frobenius method won't work)

I am sure most of you are familiar with the equation: m(x)''+c(x)'+k(x) = 0. Then, we create an auxillary equation that looks like this: mr^2+cr+k = 0. And, then we find the roots of this auxillary equation, calling them r1 and r2. And, if the roots are r1,r2>0 we consider the system to be...

Reduce to the 2nd order and solve the eq. (1-x^2)y'' - 2xy' + 2y = 0 (we know that y(1) = 0) I don't know what to do here, except that I'm supposed to find y(2). I know the formulas y(2) = y(1) Int(U) dx where U = (e^(-Int(p(x)dx)) / (y(1))^2 Can I use this?

Could you give me an example of a function that satisfies scalar multiplication but not addition? more specifically, F: R^2 -> R such that F(av)=a F(v) but F(v1 + v2) != F(v1) + F(v2) The best thing I could come up with is F(x,y)= |x| . This obviously does not satisfy additivity, but...

This is a very basic question but what is the difference between isotropic and homogeneous? I mean, I can imagine a universe that would be isotropic but not homogeneous although this seems to select a preferred frame (am I worng on this?) But I don't understand how it would be possible to have a...

Homework Statement This is the result of a problem from my Quantum class, but I figure it would be best to ask in here as my question is purely a question of how to solve a certain differential equation. the equation is of the form 0=Y''-i*a*Y' + b*Y where Y is a function of t So the...