### Partial Differential Equations

See Attached Show that satisfies the partial differential equation Note: 1- are constants 2- 3- show does not mean solve the pde

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See Attached Show that satisfies the partial differential equation Note: 1- are constants 2- 3- show does not mean solve the pde

If equation A = 1 what is the greatest possible value of equation B? *(Please see attachment for equations)

Suppose that a string of length L is held fixed at one end and is being moved up and down, say with a displacement of f(t), at the other end. Assume that the string is initially at rest and has a zero displacement, and similarly, that the forcing of the string, f(t), also has a zero initial velocity and displacement. a) Write

3. Consider the PDE problem: {see attachment} Suppose v(x,y) represents the temperature of some heat-conducting material. What physical scenario could be described by this PDE problem? What does each equation mean physically? Solve for v(x,y). Your final answer should indicate how all constants are obtained from g(x).

Consider a thin rod of heat-conducting material with length L. Suppose that the rod is initially heated to a temperature of T uniformly throughout the tod, and is dropped into a bucket of ice water at t = 0. Suppose that the rod is everywhere insulated, except for its left end (x = 0), which is expoosed to the ice water. (a)

I have a circle, diameter and radius unknown. It has a chord running through the center (point "O") and the end points are on the circle. Lets call this chord "SR" This chord SR bisects another chord "TU" and TU has midpoint "K". The only other information I have is that arc angle "TR" formed by point "T" from chord TU and point

Please see attached

Please see attachment

See attachment.

Please see the attached file for the fully formatted problem. Show that the PDE ... is of elliptic type for 0<y<1and all x does not equal 0; what is it for y>1and y<0 (and all x does not equal 0)?

You have a mass-spring system, a unit impulse is applied to this system (at equilibrium,at rest) and the response is recorded and determined to be (10e^-0.1t)- (10e^-0.2t) In general terms what does the form of the impulse response function tell you about the system?

Linear Partial Differential Equation (II) Non- Homogeneous Linear Partial Differential Equation with Constant Coefficients Problem: Find the solution of the equation (D2 - D'2 + D -

Linear Partial Differential Equation (I) Linear Homogeneous Partial Differential Equation with Constant Coefficients Problem 1: Find the General solution of the equation r = a2t.

Please see the attached file for the fully formatted problems. LAPLACE TRANSFORMS (1) Calculate the following convolution products :- t t -t (a) t * e

For this problem state the menthod you used and show the work required to obtain the answer. Find the complete solution to each of the equation problem: 4y^2 - 4y^1 + y = e^(x/2) * square root of (1-x^2)

Say whether or not R is a partial order and a total order on A. Show proof. A= {a,b,c}, R= {(a,a),(b,a),(b,b),(b,c),(c,c)

In each of the following say whether or not R is a partial order on A. If so, is it a total order? a) A= {a,b,c,d}, R= {(a,a),(b,a),(b,b),(b,c),(c,c)} b) A is the set of positive divisors of 24, that is A= {1,2,3,4,6,8,12,24}, and the relation R is dividing. If B is the set of positive divisors of 24 except 1, what is the

Let R = {(1,1)(3,1)(2,2)(1,2)(3,3)(3,2)} on Z = {1,2,3} Is R reflexive? Why? Is R Symmetric? Why? Is R antisymmetric? Why? Is R transitive? Why? Is R a partial order? Why? Is R an equivalence relation?

Let R be a relation on all real numbers x, y such that x is related to y if and only if x^2 <= y^2. Is R antisymmetric? transitive? a partial order relation? Prove or give a counter example.