Coefficients Definition and 805 Threads

Homework Statement You are given that the roots of the auxiliary equation associated with the linear, differential equation \phi(D)y = 2x- 3xe^{-3x} are m = \pm2,0,0. Write down the form of a particular solution of the differential equation as predicted by the method of undetermined...

Homework Statement Hello. I'm taking a course on Mathematical Physics, based on Eugene Butkov's book. I'm having trouble solving a DE with variable coefficients to find Green's Function. The problem asks to find Green's Function through direct construction. Homework Equations...

I have the problem "Find the particular solution of 4y''+4y'+y=3xex. What would be the assumed function y? Like would it be Ax ex?

y''+9y=sin(3t) I need to solve the above using the method of undetermined coefficients. I have already found the solution to y''+9y=0 is c1(Cos3t)+c2(sin3t). The problem is finding the particular solution. From class I am aware that the general form of the solution is...

Undetermined Coefficients, just a piece i need help with please In one of the last steps in trying to find the Coefficients of Yp (particular solution), I am supposed to set coefficients of similar terms equal to each other. Here's where i need help: i have A(e^x) + (-2B-2C+2F+E)sinx +...

Hello, I know how to get the full Fourier series with complex coefficients and with real coefficients, and I know the relationship between An, Bn and Cn. However, I don't know why the relationship between them is what is it. Can someone either explain to me where the relationship comes from...

Homework Statement Your family just had anew refrigerator delivered. The delivery man has left and you realize that the refrigerator is not quite in the right position, so you plan to move it several centimeters. If the refrigerator has a mass of 180 kg, the coefficient of kinetic friction...

letsa say i have an ak = cos ( k*Pi/4) + sin(3*k*Pi/4), the signal is discrete time, fundamental period N=12. the way i would derive its x[n] is.. Sum(k=0, to 11 of: 0.5*exp(j*k*Pi/4) *exp(j*k*w*n) + 0.5*exp(-j*k*Pi/4) *exp(j*k*w*n) + (1/2*j)*exp(j*k*3*Pi/4) *exp(j*k*w*n) -...

I know how to do Frobenius on variable coefficient ODE's but only when the coefficients are powers of the independent variable. Can I do method of Frobenius on something like: y'' + e-xy = 0 ? What form would I assume a solution of? Just the regular y=sum(Akxk+r ? Thanks for the help!

Homework Statement Find a particular solution of y'' + 2y' + 5y = e^x * sin(x)Homework Equations The Attempt at a Solution Characteristic equation: r^2 + 2r + 5 = 0. Through quadratic formula, r1 = -1+2i and r2 = -1-2i, so my homogeneous equation is y_h = c1 * e^(-x) cos(2x) + c2 * e^(-x) *...

Homework Statement Harmonic oscillator is in the first excited state |1> when a constant electric field E is switched on. Find the time evolution of the wave functionHomework Equations Schrodinger equation H\Psi = E_n\Psi H = \frac{P^2}{2m} + \frac{m\omega^2x^2}{2}-qEx The Attempt at a...

Homework Statement y''+y'=g(x) fundamental set of solns. of the homog. DE is: y1= 1 , y2= e^-x If g(x) = x^2 , yp1 = ____ Homework Equations The Attempt at a Solution I actually am looking at a key to an old test my teacher gave as a review for a test. The key has the...

first off I'd like say thanks to everyone on here, I've lurked and solved many questions thanks to you guys. First post woo. Basically we were tasked to design and carryout a lab to measure the coefficients of friction between a wooden board and some random objects (teachers gone for a few...

Hi, I'm doing a question using the Fresnel power coefficients, not the Fresnel amplitude coefficients. We can use MATLAB for this, but we are given a fixed angle of incidence of 45 deg so its really just one calculation, as opposed to an earlier question where the angle varied between 0 and...

I have been researching on the net and books for some time now. I have a few tables and equations but was wondering if anyone has the one I am looking for? I'm looking for a table that lists Wavelength(nm), Extinction Coefficient(k), Absorption Coefficeint(a) and Density(d) values from ~300nm...

a\text{''}[t]+B[t]*a'[t]-A[t]*a[t]==0 a[0] = 10^-9 a'[0] = 0 a[t] = ? The coefficients A and B are variable over time. I HAVE solved (experimental and theoretical values) for the values of A and B over the time interval of interest! I attempted to solve for a[t] using NDSolve as one...

a\text{''}[t]+B[t]*a'[t]-A[t]*a[t]==0 a[0] = 10^-9 a'[0] = 0 a[t] = ? The coefficients A and B are variable over time. I HAVE solved (experimental and theoretical values) for the values of A and B over the time interval of interest! I attempted to solve for a[t] using NDSolve as one...

Homework Statement Solve using Method of Undetermined Coefficients: y'' - 2y' + 3y = 15t - 8 The Attempt at a Solution First I used the characteristic equation to solve for the homogeneous solution to get: yh = C1e-t + C2e3t Great. Now I need to find the particular. I am...

Homework Statement Find the Fourier series coefficients X_k of the periodic signal: x(t) = 5cos(6w_0t+pi/2) (digital or discrete spectrum) Homework Equations The Attempt at a Solution I am really confused with all of this and don't...

Homework Statement find a polynomial P(x) which has nonnegative coefficients. If P(1)=1 and P(5)= 426, then wast is p(3) Homework Equations P(1)= 6 P(5)= 426 P(3)= xThe Attempt at a Solution I have tried to use guess and check. I can't find a way to solve algebraically.

I am writing a paper publishing scientific data. My background is chemistry but I have taken a couple of stat classes. In my opinion, one of the biggest deficiencies in modern research publications is the improper use of statistics. I hope to avoid making this mistake, but I need your help...

Homework Statement y''' + y'' - 6y' = 36x Homework Equations y'' + y' - 6y =18x^2 The Attempt at a Solution I've integrated the third order D.E. to get a second order D.E. Solving the characteristic equation, to find a general solution, I get: y = c_1exp(-3x) + c_2exp(2x)...

Homework Statement y'' + 3y' + 2y = 24exp(-2x) Homework Equations y'' + 3y' + 2y = 24exp(-2x) The Attempt at a Solution I've solved the characteristic equation and am after the particular solution. I've let y_p = Aexp(-2x), y_p' = -2Axexp(-2x) and y_p'' = 4Axexp(-2x) When...

I'm currently reading Weinberg, see http://books.google.com/books?id=3ws6RJzqisQC&lpg=PA207&ots=Cu9twmTMTE&pg=PA207#v=onepage&q&f=false" for the relevant section. In §5.3, the coefficient functions at zero momentum (or polarisation vectors) are unique up to a Lorentz transformation and scale...

Hey I am designing a pipe system for a class and am required to calculate headloss. At one point in the design, a pipe splits into 4 smaller pipes and then these rejoin to recreate a pipe at the original pipe. I can't seem to find the loss coefficients associated with the quadfurcation and...

Hi, I'm trying to find analytical solution to an advection equation written in Spherical coordinates. It's spherically symmetric so I'm only interested in radial variances. The equation is: \frac{\partial{c}}{\partial{t}} + \frac{1}{r^2}\frac{\partial}{\partial{r}}(r^2uc) = 0 I've seen...

I have a conceptual problem regarding the following scenario: Try to imagine a triangle with two blocks on each side, attached together with a rope, and a pulley at the tip of the triangle. Block A & B are attached to each other through a rope. Blocks A & B are in static equilibrium, each on...

Homework Statement Let f be a C1 function on [-pi,pi]. Prove the Fourier coefficients of f satisfy |an| <= K/n and |bn| <= L/n n=1,2,... Homework Equations an = 1/pi * int[-pi..pi] (f(x)*cos(nx)) dx bn = 1/pi * int[-pi..pi] (f(x)*sin(nx)) dx Sorry if my form is slightly...

Homework Statement A rope exerts a force of magnitude of 21 N, at an angle 31 degrees above the horizontal, on a box at rest on a horizontal floor. The coefficients of friction between the box and the floor are s=0.55 and k=0.50 . The box remains at rest. Determine the smallest possible mass...

Homework Statement Given the first cycle of a waveform: f(t)=2u(t)-2u(t-1)+u(t-2)-u(t-3) -- Plot the first cycle of the wave form -- Find the Fourier Coefficients Homework Equations Given above The Attempt at a Solution No idea yet. Will appreciate any help.

Here is a paper written by me: http://www.voofie.com/content/84/solving-linear-non-homogeneous-ordinary-differential-equation-with-variable-coefficients-with-operat/" Basically, it uses operator method to solve linear non-homogeneous ordinary differential equation with variable...

Homework Statement A certain metal whose thermal expansion coefficient \beta is 5,0 × 10^-5 °C^-1 and whose isothermal compressibility \kappa_T is 1,2 × 10^-6 atm^-1 is at an initial pressure of 1 atm and an initial temperature of 20°C. A thick layer of Invar is thermally insulating the...

Trying to self-teach myself more quantum mechanics. Reading Zare's "Angular Momentum- Understanding Spatial Aspects in Chemistry and Physics". I don't really understand how to calculate eigenvalues of J using CG coefficients (I mean, I know the eigenvalues of J, just trying to calculate them a...

Homework Statement Find integers a,b, and c such that m^{3} = a*nCr(m,3)+b*nCr(m,2)+c*nCr(m,1) for all m. Then sum the series 1^3+2^3+3^3+...+n^3 Homework Equations I think I need to use m^{3} = a*nCr(m,3)+b*nCr(m,2)+c*nCr(m,1) and...

Hey folks! I am studying from a thermodynamics text (engineering thermo) and I am a little confused with the wording in the following development of the "Equation of Reaction Equilibrium": I am a little confused as to the distinction between the n's and the v's. Is it saying that the n's are...

Good morning, I'm calculating the pressure loss of a ventilation system for pot-off gas of an aluminum smelter using ASHRAE tables for fitting loss coefficients. The problem is that for much of the ducting, the diameters and flowrate ratios I have do not exist in the tables. (We're talking...

Title should read "Combining", is there anyway a moderator could alter that so the search function isn't messed up? Homework Statement The Attempt at a Solution I am familiar with both methods, however combining the two is foreign to me. Anyone have any suggestions for this ODE? My...

Can anyone help me to get the general solution of the linear partial differential equations with variable coefficients of any order?

Homework Statement Problem #4 from here: http://www.math.washington.edu/~jtittelf/ExtraCredit.pdf Homework Equations ? The Attempt at a Solution There's only one example of using undetermined coefficients in my textbook. I'm not sure where to start. x = t2a + tb + c ? That's...

Homework Statement Derive a formula of the form \int\stackrel{b}{a}f(x)dx \approx c_{0}f(a)+c_{1}f(b)+c_{2}f'(a)+c_{3}f'(b) that is exact for polynomials of the highest degree possible. Apply a change of variable: y=x-a Homework Equations The Attempt at a Solution I don't get the "highest...

http://img243.imageshack.us/img243/156/55139700.png Knowns Well I know that \sum \frac{1}{1-x} = 1+x^{2}+x^{3}... I know the integral is [PLAIN]http://www4a.wolframalpha.com/Calculate/MSP/MSP32919a6dgiib73geda500000hd72bah4i062h1b?MSPStoreType=image/gif&s=36&w=241&h=38 I've...

I'll make this post short. The problem just asks me to something in the form x'=Ax (A is a 2x2 of constants) and then describe the behavior of the solution as t approaches infinity. My solution is x=C1e-2t(2/3 1)T + C2e-t(1 1)T. Since both vectors are multiplied by 1/et, my solution...

Homework Statement Given are the points (1,-4), (3,0), and (4,1). I am to usemethod of undetermined coefficients. Homework Equations Given these points I am to find a quadratic equation. The Attempt at a Solution Sorry! But I really do not have any clue. May anyone help me?

I understand permutations, combinations and such, but I can't seem to make sense of binomial coefficients, or at least the notation. As an example, could someone walk me through the notation for a generic problem.. something like 100 people eligible for an award and the winner can choose 1...

Homework Statement Find the unique solution to the differential equation y''+4y'−5y=−435sin(2t) satisfying the initial conditions y(0)=29 and y'(0)=47 The Attempt at a Solution So (I think) I found the correct general solution. I let y(t)=Acos(2t)+Bsin(2t) and eventually worked...

Homework Statement Find the Clebsch Gordon coefficients of 1/2 \otimes 1 = 3/2 \oplus 1/2 Homework Equations We have some properties of the CG coefficients which might be useful: 1) they are nonzero only if j is between j1-j2 and j1+j2 2) m = m1+m2 for nonzero coefficients 3)...

Hello mathematicians, I'm creating a program and I need in this program to rotate some planes around the origin, while I'm given the coefficients a,b,c and d for this plane, they represent a plane of the form: a x + b y + c z = d So these coefficients are given and I want to rotate the...

Homework Statement y''-49y=7cos(7x)+7+e^(7x) The Attempt at a Solution I have no idea how to solve this Differential equation. I could solve one that has y''-49y=one term, but I'm stumped with more than one. First, I get the homogeneous equation, y''-49y=0 and fine y_c, then use the...

I am working on a section on undetermined coefficients of a difference. I'm really trying to understand the material, but am struggling. y_{n+1}-2y_{n}=2 I got as far as saying for the homogenous equation y=c_{1}(-1)^{n}. I'm assuming the guess next would be A, but I'm confused. Maybe if...

Homework Statement y''-4y=60e4t y(0)=9 and y'(0)=2 Homework Equations none in particular The Attempt at a Solution First I solved for the auxiliary equation. r2-4r r(r-4) r=0, 4 So the general solution for the homogenous form is C1e0x+C2e4x where C1 and C2 are unknown coefficients to...