Parameters Definition and 489 Threads

Ok here's my problem: 1. Solve the inhomogeneous second order de: x^2y" - 3xy' + 4y =x^4 2. Worked: y(p) = 1/4*x^4 Given: y(1) = x^2 y(2) = log(x)*x^2 3. I just need help getting the roots of the given de so i can determine y(h) of this de. As...

Hey all, this is a little confusing, because the "variation of parameters" that I have been taught in class is different then what I find in most texts... I have y''' + y' = tan(x) Most textbooks use the wronskian and work from there, what I was taught to do is set it up as the...

Dear All, I would like to least square fit a number of measurements using several nonlinear functions with shared parameters (similar to the advanced fitting in Origin) using Mathematica. Therefor I would be interested in an Algorithm like Gauss-Newton that fits several data-set to several...

Homework Statement Second part of Part C is: Use mathematica to draw graphs for a few values of the parameters. [ Consider the cases b > 0 and b< 0] Homework Equations I think you use the answer to Part A The Attempt at a Solution Not sure how to graph with mathematica...

Homework Statement http://img27.imageshack.us/img27/6083/variationofparametersfop.jpg

I am studying EM wave and transmission lines. I see both derive equations for propagation constant \gamma: Plane wave velocity is 1/\sqrt{\mu\epsilon} and \eta = \sqrt{\mu/\epsilon} Transmission line velocity is 1/\sqrt{LC} and Z0=\sqrt{L/C}. From that the book just to say the velocity...

Homework Statement Find the general solution of the following diff. eqn. y''(t) + 4y'(t) + 4y(t) = t^(-2)*e^(-2t) where t>0 Homework Equations General soln - Φgeneral(t) + Φparticular(t) Wronskian - Φ1(t)Φ22'(t) - Φ2(t)Φ1'(t) The Attempt at a Solution I'm solving by...

Homework Statement y''+y=tan(x)+e^{3x}-1 Homework Equations homogeneous solution: y_{hom..}=C_{1}cos(x)+C_{2}sin(x) particular solution: y_{parti..}=v_{1}' cos(x)+v_{2}' sin(x) The Attempt at a Solution v_{1}' cos(x)+v_{2}' sin(x)=0 (1) -v_{1}' sin(x)+v_{2}' cos(x) =...

Would like to replicate a project we did in school for Turbomachinery class, which was to build a functioning hydropower turbine model. We were given the varous ideal parameters like bucket width, width to length ratio,number buckets and nozzle diameter based on size of wheel. Anyone know of any...

Problem:IF there is heat radiation within the rod of length L , then the 1 dimensional heat equation might take the form u_t = ku_xx + F(x,t) Find u(x) if F = x , k = 1 , , u(0)=0 , u(L) = 0 the problem is that i am not sure what this is asking me , how can i find u(x) if i have...

I'm working on some calculations on Al0.35Ga0.65As & In0.65Al0.45As. Someone can tell me where i can find the elastic/piezoelectric/dielectric constants for these rare alloys?? A database for them exist for us to search?? Thx...

Hi, When using the method of variation of parameters to solve something like; y'' + y' = 2^x I got the aux. equation: r^2 - r =0 which gives the roots r=0,1 How do I find the complementary equation yc?

http://arxiv.org/abs/0812.2720 Chandra Cluster Cosmology Project III: Cosmological Parameter Constraints A.Vikhlinin, A.V.Kravtsov, R.A.Burenin, H.Ebeling, W.R.Forman, A.Hornstrup, C.Jones, S.S.Murray, D.Nagai, H.Quintana, A.Voevodkin ApJ, in press: Feb 10, 2009 issue (Submitted on 15 Dec...

Consider, x' = x + 3y^3 y' = -3y I am trying to use the fundamental matrix, F(t), and 3y^3 as my g(t) in order to plug into the variation of parameters formula... Xp = F(t) * \integral{ F(t)^-1 * g(t) } , Am I going about this the wrong way? I am trying to get...

Hi I know that our world is quite unstable and minor changes in these parameters could make the existence of life impossible. However, I am interested in what exactly is going to happen if we start to increase/decrease any of 30 parameters. It is interesting how well-tuned these parameters...

What is "Variation of Parameters"? Homework Statement None. General. Homework Equations I don't know. :( ? The Attempt at a Solution ? I am taking a class right now on engineering analysis (which I am finding it to be more like partial differential equations mixed with...

I want to calculate the electrical parameters of solenoid coil of a valve for a given spring force. I know the force required to pull the solenoid plunger through a given distance against a spring, is there any formula to find out the required voltage, number of turns of coil winding & current .

Ive taken a general relativity course and in it we learned about how black holes are characterized by the parameters of mass, angular momentum, and charge. I have some questions about other parameters though. 1) Can a black hole have a vibrational parameter? This would really only be...

Homework Statement y''+2y'+y = 4t^2 - 3 + (e^-t)/t of course i evaluated the general soltuion to be c1e^-1t + c2te^-1t but now how do you do the right part? i tried y=At^2+Bt+c+1/(Dt+E)*e^-t as a solution but after differentiating it twice and putting it into the eqaution i got...

Question is attached as Clipboard01.jpg I have tried the use Variation of Parameters to solve this question, but I kept getting wrong answer. This is What I get y=(2e^x)(Cos(e^x))+0.5(e^(-x))Cos(e^(-x))-2Sin(e^(-x)) This is the right answer: y=-Sin(e^(-x))-(e^x)Cos(e^(-x)) Procedure is...

cavity on a water surface A vertical air jet from a straw produces a cavity on a water surface. What parameters determine the volume and depth of the cavity?

Hi I'm trying to get comsol multiphysics to first define an inline function with 1 variable and 4 parameters, and then run fzero on that same function. I can do it with two parameters, but no moore. This works: clear myfun=inline('exp(y).*cos(x)+z', 'x', 'y', 'z'); x1 =...

Homework Statement Io, a satellite of Jupiter has an orbital period of 1.77 days and an orbital radius of 4.22 x 10^5 km. From this Data determine the mass of Jupiter Homework Equations 4pie^2/GM Kepler's Third Law The Attempt at a Solution I keep getting turned around. I know the...

As the name suggest, this problem is an undetermined coefficients problems where variation of parameters is necessary to solve. As with my previous question; This is not a homework problem, but it is out of the textbook so I figured this would be the appropriate place to ask if I am doing it...

Homework Statement Decide c, so that A(2)X=b(c) where x=(x,y,z) and b(c)=(1,c,1) A(2) is calculated from the previous problem: "Decide the value on the parameter b so that the following system has solutions (2, 1,-1,b 1, 2, 2, 2b 1,-1,-3, b+1) Homework Equations The...

Homework Statement 2y\prime\prime +2y\prime + y = 4 \sqrt{x}The Attempt at a Solution charecteristic equation: x^2+x+\frac{1}{2} roots: \frac{1}{2}\pm\frac{1}{2}i homogenous solution: a \sin{\frac{1}{2}x} + b \cos{\frac{1}{2}x} Wronskian...

Why do we look at the probability of a given data set given the parameters, as opposed to the probability of the parameters given the data set? So y(x) = y(x;a_{1} \ldots a_{M})

How do you calculate lattice parameters c and a of Hexagonal ZnO ? if you are given the wavelength= 1.5406 nm, diffraction angle= 48 and the miller indexes (102)

Let's say I have some data, as a function of a variable x. I want to fit this to the real part of the function \frac{A}{1-ix}\left(1+\sum_{n=1}^\infty\frac{c_n}{(1-ix)^n}\right) by numerically fitting the first N of the c_n's (A is fixed). I tried something like A = 1; N = 100; fit...

[SOLVED] Variation of Parameters Homework Statement y^(4)-6y^(3)=-5sinx The Attempt at a Solution I factored this at x^3(x-6)=0 so my r values are 0,6 also using for y(p) Dcosx + Esinx y=Ae^0 + Be^6x + Dcosx + Esinx ? y' =6Be^6x -Dsinx + Ecosx y'' =36Be^6x-Dcosx - Esinx...

Homework Statement Okay so when solving a system of D.E.s using Variation of Parameters I know that first I find the complementary solution Xc and then do a bunch a of crap after that using the fundamental matrix. Now I just came across a problem with repeated roots, so I just want to...

So I pretty much have this Differential Equation solved except that I have to integrate the expression \int \Phi(t)F(t)dt it has a star next to it in my attached work. Does this look readily integrable to anyone? For some reason nothing is ringing a bell. I suppose I could go by parts, but...

Does anyone know about the parameters that affect the design of fan? For example, is there an optimum number of blades, or optimum curvature and shape for the blade? I suppose this has to do with fluid mechanics (which I know nuts)? Which particular equations am I looking for? Is there any book...

Solve by method of variation of parameters (x^2)y'' - (4x)y' + 6y = x^4*sinx (x > 0) Hey, I know how to solve problems using variation of parameters but only when the corresponding homogenous equation has constant coefficients... y'' - (4/x)y' + (6/x^2)y = 0.. the bit I am confused about...

Homework Statement Use the method of variation of parameters to determine the general solution of the given differential equation: y^(4) + 2y'' + y = sin(t) Homework Equations characteristic equation is factored down to (r^2 + 1)^2, so r = +/- i. this gives the general solution to be...

Why can't i send parameters to an IDC(I.D. Control) I'm programming a MFC project in C++ using Visual Studio. I'm trying to send 2 parameters through an IDC, so the values of these variables can past through other methods, but i keep getting an error message:error C2440: 'static_cast' : cannot...

WMAP2006: Cosmological Parameters and Large-scale Structure of the Universe So that makes \Omega_{Total} = 1.014 - a just closed universe with spherical spatial geometry. You can get the range of best fit values from Table 3 of that paper, they do not seem to include the flat space model...

Hi, I need to calculate the parameters of the following equation: S = (a + ((b-a)/(1+((2*pi*x)^2*c^2)))) I have the measured data of S and need the parameters a,b and c to get a curve fit in the software for analysis. If someone can help me in this regard or suggest any software that...

I wonder: Is it possible to find a function f(x) which satisfies this integral for *arbitrary* parameters a,b (but maybe of known domain)? \int_{-\infty}^\infty e^{-x^2}f(ax+b)\mathrm{d}x=0 I want f(\pm\infty)=0 and I can deduce \int_{-\infty}^\infty x^n e^{-x^2}f^{(m)}(ax+b)\mathrm{d}x=0 It...

Within the description for the variation of parameters procedure is the restriction: y1u1' + y2u2' = 0. Can you explain this restriction, it is not obvious to me, I do not have an explanation where this comes from. Is it related to u[ \frac {dy}{dx} + P(x)y] = 0 from solving first...

Greetings, Regarding the two procedures: undetermined coefficients and variation of parameters, can both procedures be used interchangeably - meaning they both solve (non-homogeneous linear equations)? Does one method work better in certain situations, if so which method is preferred when...

Homework Statement I've created a function inside IDL and I want to be able to specify the binsize. That is, I want to have: result = myfunction(array, keyword) Whenever I add the keyword in the brackets there it says: "Keyword parameters not allowed in call." 2. Relevant code...

Well, i really i am pissed at the moment because of this. I have been trying to figure out if there is a proof/justifaction for the method of variation of parameters and have had absolutly no luck. I have searched the internet and almost every differential equation books in my university library...

In our exchange previous to my guest post, Dorigo suggested me to speak of decay rates, but I did not take the courage to extend about this topic. Still, it is an interesting one for a whole thread here, and see what are the ideas of the people of PF. to start with, I think some dimensional...

Homework Statement A spy satellite is in circular orbit around Earth. It makes one revolution in 6.00 hours. (a) How high above Earth's surface is the satellite? ________ km (b) What is the satellite's acceleration? ________ m/s2 Homework Equations GMm/r^2 = m(v^2/r) The...

Thanks to EnumaElish for helping me in Normalizing the histograms. I now want to find the best fit distribution and what will be the parameters for that distribution. I tried lograthmic but it goes in negative and also is not much fit (the new plots are attached). If I use poisson what will be...

Homework Statement x^2y''-2xy'+2y=x^3cosx Find a general solution by using variation of parameters 2. The attempt at a solution I already solved this one, but I have 4 questions: 1. I found the solutions x and x^2 to the homogeneous equation by inspection. Is this the only way to...

In my previous classes we did just a bit of 2 port stuff. Where you shorted one port and then you just divided port 1's current by port 1's voltage and bam. Now we're starting to learn about n port microwave networks, and I really want to know what's going on. This post will probably be...

Hello, I have the following doubt, maybe someone can help me with this. Suppose I have a general purpose routine that finds the zero of a function f(x), something like subroutine fzero( func, x1, x2, xzero ) implicit none real, intent(in) :: x1, x2 ! Upper and lower bounds where the...

silly question. didnt know where it was meant to go so i just put it here as safest option:) suppose a curve C is defined by, r(t) = (sint, cost) with 0 \leq t \leq 2\pi if a sketch of C was required then would you simply just draw the graphs for sint and cost?