### Initial value problem

Consider the initial value problem on [1,2]: x^2*y'' + xy' - K^2*y = 0, y(1) =1, y'(1)=0 Find the solution y(x,K). Is it a continuous function of K? Can it be differentiated with respect to K? K is a constant

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Consider the initial value problem on [1,2]: x^2*y'' + xy' - K^2*y = 0, y(1) =1, y'(1)=0 Find the solution y(x,K). Is it a continuous function of K? Can it be differentiated with respect to K? K is a constant

Determine each of the following based on the relation {(-5, -3), (-2, 1), (2, 2), (-5, 8)}. 1. Is the relation {(-5, -3), (-2, 1), (2, 2), (-5, 8)} a function? 2. Identify the domain of the relation {(-5, -3), (-2, 1), (2, 2), (-5, 8)}. 3. Identify the range of the relation {(-5, -3), (-2, 1), (2, 2), (-5, 8)}.

(See attached file for full problem description) Please help with the following questions: 4, 12, 16, 24, 36, 38, 42, 48, 50, 60, 66

Using MATLAB, obtain the unit-step response of the following system: C(s)/R(s) = 10/s^2 +2s + 10 where R(s) and C(s) are Laplace transforms of the input r(t) and output c(t), respectively. Hint: Use the following command; step(num,den)

We are using the book Methods of Real Analysis by Richard R. Goldberg (See attached file for full problem description) --- 12.6-3 Let be a complete orthogonal family in . Define the function A from into .( This means: In order to manufacture our metric space we must therefore regard any two function whose valu

USING THE BESSEL FUNCTION OF ORDER ZERO: Verify that it is the solution to the differential equation x^2 y'' + x y' + _x^2 y = 0, satisfying y(0)=1, y'(0)=0. Here y' means the first derivative of y(x) and y'' means the second derivative.

Give an example (and explain why it works) of an analytic function u on a harmonic function v such that the composite function u o v is defined but NOT harmonic. Please see the attached file for the fully formatted problem.

On the following terms could you please give my an English text description - in your own words. Thanks. 1. Sequence 2. Geometric Progression 3. String 4. Recursive definition of a function 5. Recursive definition of a set 6. Recursive algorithm 7. Program correctness 8. Loop invariant 9. Final assertion

This involves the Bolzano-Weierstrauss Theorem, I believe, but I'm not sure where to start. Prove that the set of open disks in the xy plane with center (x,x) and radius x > 0, x rational, is a countable covering of the set {(x,y): x > 0, y > 0}

Given f(x,y)=x3+3xy2-3x2-3y2+4. Find all critical points of f and find extreme values (maxima and minima) and saddle points of f. Please see the attached file for the fully formatted problems.

Solve 1. X + 3 - X+ 4 = X + 5 - X + 6 X + 2 X + 3 X + 4 X + 5 2. Higher education French language registration in the USA from 1970 to 1998 can be modeled with the quartic function f(x) = 0.004X - 0.2268X + 5.836X - 46.121X + 360.046, where f is in thousands and x is the number of years since 1970. Use th

Given the cost function C(q) = 4000 + 50q + 0.002q2 and the demand function p = 80 - 0.025q, find the value of q for which: (a) Average cost is a minimum. (b) Revenue is a maximum. (c) Profit is a maximum. ---

1. Let g: R→R+ be such a function that g∈ C^1(R) and for all x ∈ R, -1 <g'(x) < 0. Show that the sequence Xn+1 : = g(Xn) converges to the unique fixed point of the function g, regardless of chioce Xo ∈ R. [ Note : Observe that the domain of function g is not a compact interval.] 2. Write a matla

Determine if the following functions satisfy local or uniform Lipschitz condition. 1). te^y My work: I found d/dy (te^y) = te^y, and this is not bounded above for any value of y, so this made me conclude that it has locally Lipschitz condition since the Lipschitz constant here changes as the reagion changes? Am I right?

School is about to begin. The janitor has all the lockers closed. All 1000 of them. Student #1 comes along and opens ALL of the lockers. Student #2 comes along and closes doors 2, 4, 6, 8, 10, etc.... Student #3 comes along and changes the state of every 3rd locker ( 3, 6, 9, 12, 15). Student #4 comes along and c

Real Analysis Jacobians(I) Necessary and sufficient condition for the value of a Jacobian of n independent functions to be zero The fully formatted problem is in the attached file.

I need to use separation of variables to solve Laplace's equation in the annular sector: 1< r<2, 0< theta< pi/2, u(1,theta)= f(theta), u(2,theta)=0, u(r,0)=0, u(r,pi/2)=0 Thank you!

The average numbers of home runs hit by the Boston Red Sox per game are: 2 divided by 3 = .66 5 divided by 2 = 2.5 6 divided by 1 = 6 7 divided by 0 = 0 Is that correct using the weighted approach?

Having trouble researching the number of deaths in the US each year due to each of the following medical conditions in each of these years: 1985, 1990, 1995, and 2002. heart disease, cancer and aids e.g. The websites keep bringing up different types of cancer, nothing is specific. Totally frustrated... e.g. 1980 throug

The problem is from Numerical Methods. Please show each step of your solution and tell me the theorems, definitions, etc. if you use any. Thank you. Start with P0 = 0 and use Jacobi iteration to find..... (Complete problem found in attachment)

A mass 5kg is attached to a spring suspended from the ceiling. When the mass comes to rest at equilibrium, the spring has been stretched 2m. The mass... Determine the motion of the mass. Decribe its motion in as much detail as possible. Please see attached.

(g o f) (1) let f(x)= 2x-3, g(x)= x2 + 3

Let [EQUATION1] with [EQUATION2] and [EQUATION3]. The idea is to write each such set in some simple canonical form. (i) When n = 2, how many distinct knapsack sets are there? Write them out in a canonical form with integral coefficients and 1 = [EQUATION4]. (ii) Repeat for n = 3 with [EQUATION5]. *(For proper equations an

See attached, ps explain correct answer

5. The faces of a 3-regular polyhedron are all squares or hexagons. How many square faces can the polyhedron have? Does the number of square faces uniquely determine the polyhedron? (Please see attachment)

Suppose that a population develops according to the logistic equation: dP/dt = 0.15P - 0.003P^2 where t is measured in weeks. what is the carrying capacity?

Using the numbers 3, 3, 8 and 8 once and only once, obtain the target number of 24. (You have to use 3 twice and 8 twice - 3 x 8 = 24 is not acceptable). You may use only addition, subtraction, multiplication and division (eg. no factorial). Hint: no addition in the equation.

Find the composition of the following cycles representing permutations on A = {1,2,3,4,5,6,7,8} Answer as a composition of one or more disjoint cycles. A) (1,3,4) . (5,1,2) B) (2,7,8) . (1,2,4,6,8) C) (1,3,4) . (5,6) . (2,3,5) . (6,1)

Show that a) e^(t^2) is not of exponential order, and b) e^(t^1/2) is of exponential order

See attachment Given f(x) = sqrt(x^2) -1 g(x) = 2/x Find (gof)(x).