Coefficients Definition and 805 Threads

Homework Statement the problem is to solve this differential equation: x^2 y'' + xy' + (4x^2 - 1)y = 0

Hi guys, I need the dynamic friction coefficient between steel and teflon. Do you know where I can get it? Thanks

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Homework Statement Decide whether or not the method of indetermined coefficients can be applied to find a particular solution of the given equation: The attempt at a solution I think the answer is yes, because the equation is of the form: a\ddot{y}+b\dot{y}+cy=F(t)where F(t) is the...

Fix some constant 0<\alpha \leq 1, and denote the floor function by x\mapsto [x]. The conjecture is that there exists a constant \beta > 1 such that \beta^{-n} \sum_{k=0}^{[\alpha\cdot n]} \binom{n}{k} \underset{n\to\infty}{\nrightarrow} 0 Consider this conjecture as a challenge. I don't...

Homework Statement Find the solution of the given initial value problem. \[y''-2y'-3y=3te^{2t}\]Homework Equations The Attempt at a Solution(1) the homogenous solution is given by \[y_{h}=c_{1}e^{3t}+c_{2}e^{-t}\] (2) the particular solution is in the form \[y_{p}=(At+B)e^{2t}\] (3) The...

for a system defined as y(n) + a1y(n-1) + a2y(n-2) = bx(n), for what values of a1, a2, and b is the system realizable? i know that the transfer function is obtained by the following H(z) = Y(z)/X(z) H(z) = b/(1 + a1z-1 + a2z-2) H(z) = bz2/(z2 + a1z + a2) i also know that the poles have...

Homework Statement An electron with kinetic energy 5 eV (8.01E-19 J) passes through a 3 eV (4.806E-19 J) potential barrier. There are certain widths for this potential barrier in which the transmission probability will equal one hundred percent and the reflection probability will equal zero...

Homework Statement y" + y = 2/sin(x) solve for y Homework Equations I tried to use variation of parameters to solve this but I don't know how to check it. The Attempt at a Solution y = -2xcosx + (constant)cosx + 2ln(sin(x))sinx + (constant)sinx How do I do this using...

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...

Homework Statement Hi. I have this problem, which says: The equation x^2y''+pxy'+qy=0 (p and q constants) is called Euler equation. Demonstrate that the change of variable u=\ln (x) transforms the equation to one at constant coefficients. I haven't done much. I just normalized the equation...

Homework Statement The function f(x)=ln(10-x) is represented as a power series: \sum^{\infty}_{n=0}a_{n}x^{n} Find the first few coefficients in the power series. Hint: First find the power series for the derivative of . The Attempt at a Solution Okay, start seems fairly...

Does the variable coeffcient in linear differential equations have to be polynomials? All the examples I have found seem to be polynomials for example the Cauchy–Euler equation. For example is sin(x)y'' + cos(x^2)y' + y = 0 still considered a linear differential equation with variable...

Homework Statement Calculate [x^n] (1-2x+x^2)^{(-k)} Homework Equations Just the geometric series.The Attempt at a Solution This is what I got so far [x^n] (1-2x+x^2)^{(-k)} = [x^n]((x-1)^2)^{(-k)} = [x^n] \frac{1}{(x-1)^{(2k)}} Basically, how do I put this into a sum form? or can I just...

Hi, everyone: If we change the coefficients used to calculate homology, the universal coefficient theorem tells us how the homology changes. Still, is there a way of knowing whether a specific (non-trivial) cycle under certain coefficient is still a cycle after the coefficient...

Homework Statement y-(sinx)2)dx + sinx)dy Homework Equations Since the result wouldn't be a line, the equation would only be linear in one of its variables. The Attempt at a Solution y-(sinx)2 = 0 ; sinx = 0 --- y = (sinx)2 + sinx No clue... Also, is there more than one way to...

Homework Statement The following is the output of a 16 point computation of the discrete Fourier Transform for data taken at 10 kHz. Complete the table below by determining the frequencies associated with each of the FFT values. I attached an Excel workbook with the table. Homework...

Hi. I'm trying to make a simple model of a condensation based countercurrent heat exchanger where liquid water and steam flows are separated by a conducting wall. I formed the equations as Q = \frac{T_{steam}-T_{water}}{\frac{1}{Ah_{water}}\frac{d}{Ak_{wall}}\frac{1}{Ah_{steam}}} = L\dot{m}...

have been solving PDEs by sep of variables, and the solution that comes out is generally a summation the general look of it is something like: U=SIGMA(n=1 to infinity)E_n(sin(n(pi)x/L)(cos(n)(pi)x/L)t The above may not be exactly right, I was thinking along the lines of heat equation where...

Hi all! I'm trying to solve the following system of ODE's, but somewhat unsuccessful... \dot \vec x = [-i\omega(t)\sigma_z - \nu(t)\sigma_y]\vec x with sigma_i the Pauli matrices and w(t) and v(t) well-behaved functions of t (actually I also have that w = 1+v). Nevertheless, v(t+T) =...

Homework Statement Hi... Don't know if it's actually homework, since it's not, but I hope it's okay to post in here. I am looking for a paper/website/article of some sort, that might have the derivations of the above mentioned coefficients ? It's for calculating the figure of merit...

y''-2y'-3y=-3te^-t i know that that the general solution to this problem is yh = c1e^3t + c2e^-t i am having trouble figuring out what the particular solution is (yp) i keep getting the yp = 3/4te^-t , but wolfram alpha is telling me that the answer is something else. how do i get...

Homework Statement Prove that a polynomial f of degree n with coefficients in a field F has at most n roots in F. Homework Equations The Attempt at a Solution So we could prove this by induction by using a is a root of f if and only if x-a divides f. My question is: why do...

Hi everyone I'm modeling the dynamics of a cantilever that has a non-constant linear density profile, i.e. \rho(x)=\rho_{1} \0 \leq x \leq x_{0} \rho(x)=\rho_{2} \0 x_{0} \leq x \leq l \rho(x)=0 \0 otherwise My differential equation is: \frac{ d^4 \phi(x) } {d x^4} = \phi(x)...

I'm working on undetermined coefficients for nonhomogeneous equations. I have an equation that is equal to 3xe^x. For an earlier one that was equal to e raised to 8x, I used Ae^8x; but on this one, obviously that won't work. I don't know what I should be looking at. I tried Axe^x but no dice...

http://www.cs.odu.edu/~toida/nerzic/content/problem_solving/problem_solving.html example 3 ========================================= Quote Problem: Given that a, b, and c are odd integers, prove that equation ax2 + bx + c = 0 can not have a rational root. Understanding the Problem: This is a...

Homework Statement Find the Clebsch-Gordan coefficients associated with the addition of two angular momenta j_1 = 1 and j_2 = \frac{1}{2} Homework Equations The table of coefficients. The Attempt at a Solution I think I am misunderstanding something important here. I can't see...

Homework Statement Set up but do not solve for the appropriate particular solution yp for the differential equation y''+25y=2xsin(5x) using the Method of Undetermined Coefficients (primes indicate derivatives with respect to x). Homework Equations The Attempt at a Solution I first solved the...

I am trying to find the Fourier coefficients for the following signal: For some reason, I keep getting 0, which doesn't make sense to me. I am even getting 0 for F0 even though there is clearly area under the curve. Here's my work for this part: Period = T/2 Natural freq = 4pi/T F0 =...

Let V be the space of polynomials of degree 3 or less over \Re. For every \lambda\in\Re the evaluation at \lambda is the map ev_{\lambda} such that V \rightarrow \Re is linear. How do we find the coefficients of ev_{2} in the basis dual to \{1,x,x^2,x^3\}?

Hi all, I have run a few linear regression models predicting water quality for watersheds using explanatory variables such as mean impervious surface within watersheds and others suggested by theory and the research of others. I would like to be able to compare explanatory variables measured...

The eigenvalue problem of Schroedinger equation can be solved in a variety of ways. The continued fraction method can be stated by the following recipe: - represent the solution of the D.E. as a power series - replace back this solution into the D.E. - obtain a three term recurrence relation...

Right so basically, I'm doing a multicomponent distillation with some exotic chemicals. My feed comes in at 13kPa and 60*C, so it's under vaccum. This will be a two phase mixture. What I need is the vapour-liquid-equilibrium coefficients, 'K- values' at feed conditions. I'm basing this on an...

Homework Statement Solve the quadratic equation z^2 + 4(1 + i(3^0.5))z - 16 = 0 Homework Equations The Attempt at a Solution I think I've done this correctly, I just wanted to verify. I've only done the solution for k=0...

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...

Homework Statement Find the solution of the equation v''- 4v'+5v=0,such that v=-1 and v'=1 when x=pi=3.14159Homework Equations ... The Attempt at a Solution I treat it as a polynomial=>r^2+4r+5=0 =>delta=-4=>r1=2+2i and r2=2-2i v=e^[x+2](A*cos[2]+B*i*sin[2]) v=-1=e^[pi+2](A*cos[2]+B*i*sin[2])...

Given the difference equation a_{n+2}+A_n(\lambda)a_{n+1}+B_n(\lambda)a_n=0 where A_n(\lambda)=-\frac{(n+1)(2\delta+\epsilon+3(n+\gamma))+Q}{s(n+2)(n+1+\gamma)} and B_n(\lambda)=\frac{(n+\alpha)(n+\beta)}{2(n+2)(n+1+\gamma)} The asymptotic behavior of the...

I'm kind of stuck in my search, hoped to be able to find some answers on this board. Anyways, I've been taksed to design a slow speed mixer and I'm trying to look up information beyond Stokes Law of FD = 6 pi r V u The fluid to be mixed is approx. 100000 poise, incompressible fluid. I'm...

Homework Statement Show that if the polynomial p(z)=anzn+an-1zn-1+...+a0 is written in factored form as p(z)=an(z-z1)d1(z-z2)d2...(z-zr)dr, then (a) n=d1+d2+...+dr (b) an-1=-an(d1z1+d2z2+...+drzr) (c) a0=an(-1)rz1d1z2d2...zrdr Homework Equations Taylor form of a polynomial? p(z) = \sum...

x y'' + (x + 1) y' = 2 x Solve for y(x). Due to the coefficients being a function of x, I have no idea where to start to find the homogenous solution (Complementary Function). I know how to proceed after this part with the variation of parameters method. I just have no idea where to...

Homework Statement Find and prove a formula for sum{ (m1 choose r)(m2 choose s)(m3 choose t) } where the sum is over all nonnegative integers r, s, ant t with fixed sum r + s + t = n. Homework Equations The Attempt at a Solution I first attempted to find the number of combinations of r...

Hi Few months ago, I had written to PUMA, ADIDAS, NIKE etc. for the shoes with high coefficients of static friction, so that I can make more informed decision when I go to these shops next time. None of them replied. I know that, these big companies do a lot of research on the shoes. They...

Homework Statement Prove that for an integer n greater than or equal to 2, nC1 - 2nC2 + 3nC3 - + ... = 0. (nCm means n choose m) Also, 2x1 nC2 + 3x2 nC3 + 4x3 nC4 +... = n(n-1)2^(n-2) Homework Equations (1+t)^a = 1 + aC1(t) + aC2(t^2) + ... The Attempt at a Solution I don't know...

If we have a vector that can be expressed in terms of some finite list of basis elements. If we have an orthonormal basis for a vector space V, then a vector v can be expressed as <v,e1>e1 +...+ <v,en>en. This appears to be widely used for many results (such as Gram-Schmidt), but the...

Homework Statement Argue that if y=f(x) is a solution to the DE: y'' + p(x) y' + q(x) y = g(x) on the interval (a,b), where p, q, and g are each twice-differentiable, the the fourth derivative of f(x) exists on (a,b). Homework Equations The Attempt at a Solution Its a general...

Homework Statement For t\in\mathbb{R}, let: A=\left[\begin{array}{ccc} -1 & 0 & 0\\ 0 & 2 & 2t\\ 0 & 0 & 2\end{array}\right] Get the solution for the general equation: X'=A(t)X Homework Equations The Attempt at a Solution I done many of these problems, all with constant...

How to calculate 1) binomial coefficients and 2) binomial distribution on a Casio fx-9860G calculator?

Hello! How do I prove ? Thank you! (it can be proven by using the convergence of the Fourier series in L_p-norm, but I want to use the above result to prove the convergence in L_2-norm, so I want to avoid that)

Correct me if I'm wrong. :) I'm starting to learn basics of the ordinary differential equations, and I have some troubles understanding the concept and method as a whole. I understand when to use the method of undetermined coefficients (MUC) as opposed from variation of parameters. Suppose...

I have a three term recurrence relation \[ a_0=1, \] \[ a_1=p_1(1)a_0, \] \begin{equation}\label{recurr} \begin{array}{ccc} a_{n}=p_1(n) a_{n-1}+p_2(n) a_{n-2}, && n\ge2.\\ \end{array} \end{equation} where \[...