# parameters

1. ### Variation of Parameters work check

Can someone check my work and see what I did wrong. This is an initial value problem. Here's the question and my answer: Here's my work. Sorry if it is hard to read.
2. ### How to calculate rate of future population decline with loss and gain parameters?

I need help figuring out what I think is an algebra problem, but I don't know how to set it up. I have a population starting at 1.6 billion. The annual growth rate is 2%. The annual mortality rate is 0.6%. The problem is this: In addition to the above parameters, there is a constant loss...
3. ### Trouble understanding method of variation of parameters

Problem: y'''-3y''+4y = e^2x, solve using method of variation of parameters. Aux polynomial: r^3 -3r^2+4 = (r+1)(r-2)^2 therefore Y(homogeneous) = ae^-x + be^2x +cxe^2x. Now normally I would just take a guess at the particular solution and say its of the form: Ax^2e^2x. Then I would find...
4. ### line integral parameters

Can some please help me with this question I dont understand why those certain parameters are chosen? and also why cant i just apply green's theorem directly ?
5. ### Correct statistical notation - Gamma distribution with 3 parameters

Hello! Let's say a random variable has a normal distribution with mean 10 and variance 100. An appropriate notation is: X ~ N(10,100) Similarly, a random variable X with a uniform distribution on the interval 2 and 4 may be represented by X ~U(2,4) However, I am unsure how to express that a...
6. ### how many parameters are there in general solutions?

If the coefficient matrix A in a homogeneous system of 33 equations in 28 un- knowns is known to have rank 12, how many parameters are there in the general solution?
7. ### Inequality with known minimum values of parameters

Hi! I want to show that when 0<p<1 then the inequality holds for all values of d and b that are >0. And for p>1 then the inequality does not hold for any values of d and b >0. I know the answer as I have "solved" it numerically in excel, however I do not know how to do it with algebra. I have...
8. ### Solving a DE by method of variation of parameters

I have found the general solution for the equation of y'' - 9y = (x+1) e^{-x} to be y(x) = A e^{3x} + B e^{-3x} - \frac{1}{8} e^{-x} x - \frac{3 e^{-x}}{32} by the method of undetermined coefficients. However I need to use the method of variation of parameters, but I am totally confused. I...
9. ### Continuity in each of parameters mean joint continuity in the domain?

Dear MHF members, here is my problem. Suppose that we are given a real- or complex-valued function f on a rectangular domain D:=[a,b]\times[c,d]\subset\mathbb{R}^{2} such that f(t,\cdot) is continuous on [c,d] for each fixed t\in[a,b], and f(\cdot,s) is continuous on [a,b] for each fixed...
10. ### Limits - find parameters γ, δ

Made a new thread for this as instructed by Plato. On to the limit itself \lim _{x\mapsto 0} \frac {\gamma + \delta \sin {x}}{x^2} = 3 I found this in a book with exercises and although Plato mentioned it has no solutions the book says they're γ = 6 and δ = -6 . Also I double checked it and...
11. ### Limits - find parameters α , β

I am given this limit and am asked to find parameters α and β \lim _{x \mapsto 1 } \frac{x^2 + \alpha x + \beta}{x^2 - 1} = 2
12. ### MATLAB question: using "solve" and getting rid of arbitrary parameters

I am trying to solve a system of equations whose answer will depend on arbitrary values. For example, consider the following system of 2 equations and 3 unknowns: syms x1 x2 x3 E=[x1+2*x2+x3;x3-x1+x2]; a=solve(E==0,x1,x2,x3) A=[a.x1 a.x2 a.x3] this gives me an answer that depends on an...
13. ### Choosing the right parameters in model so that it matches real data

Hello, I've got some data on an epidemic in various locations - the total number of agents and number killed by the infection after 1 year. -This gives gives me a distribution of percentages of the populations that have been killed by the infection. (but all the percentage values are...
14. ### Diagonalizing matrix problem with parameters

Hi, I have this problem I'm stuck on: A is a 3x3 matrix A= a,b,c are real numbers 1) determine for what values of a,b,c the matrix A is diagnoizable. (advice: distinguish between the cases a=c and a=\=c) My attempt at a solution has been finding det(tI-A)=0 , the characteristic polynomial is...
15. ### System of linear equations with parameters

Hi, I am wondering if anyone could help me with this system or linear equations with parameter k. I've tried using reduced row echelon form, but I'm not sure about my answer. This is the problem: x1 - x3 = -3 3x1 + 6x2 + 3kx3= 3 kx2 + 5x3= 4 2x1 + kx2 - x3= -2 Thank you for your help!
16. ### Matrix With Parameters

I have this matrix where I need to find the values for x and y such that the system is inconsistent. I tried reducing the matrix so that each row would have a pivot, but I ended up with quite a mess, Can't figure out if I am stumbling somewhere or even where to venture from here. Any hints...
17. ### Estimating parameters using a different method?

Hi, I have a probability distribution which has two parameters a and b I re-parametrized the distribution such that the new distribution has two parameters c and d where c=a but d = 1/b - 1 I can easily estimate a and b but I need to make inferences on c and d, specially d , So my...
18. ### Solving Differential Eq. with Matrices Help using Variation of Parameters

I need help solving this problem attached is the problem and my work and solution i got.. i checked it with maple and got everything right execpt there was no e^7 term.. can someone tell me where i went wrong? Thanks, P.S: I know this problem can be solved using ordinary methods of solving...
19. ### Estimator of parameters

I've got an uni assignment to do and I can't figure out one of the questions. We have to consider 2 models, the first being Y = Beta1 + Beta2(X) + u Then the second being Y = Alpha1 + Alpha2(X/100) + u We've been given a dataset: 82.1 41.3 29.2 18.5 -25.2 -29.3 27 16 57.1 61.9 29.3...
20. ### Variation of Parameters

I have a problem understanding a certain step using the Variation of Parameters Method. take for example y''+y=sec(x)tan(x) Auxiliary Equation: m²+1=0 thus m= +/- 1 CF: Y1= Acos(x)+Bsin(x) then I let y=A(x)cos(x)+B(x)sin(x) and differentiate to y'=-Asin(x)+Bcos(x)+[A'cos(x)+B'sin(x)]...