please show steps Problem 9. (5 points) Cowen met L "sta) dr – 3 " sie)dt...
(9 points) In this question, we will find E(X), the nth moment of X,, where X, N(0,0%) is normally distributed with mean 0 and variance oz. (a) (3 points) A function po() is a probability measure on R if po(t) > 0 V2 € R and Po(x) dx = 1. By showing Lee* dar = Vī, show that po(x) = 2 e is a probability measure. (b) (3 points) Completing the square, compute the moment generating function of X, V20...
Problem # 1: (70 points) Solve the following problems (a) and (b) using Laplace Transform: a) (7 points) y(0)-y'(0)-0 y"(0)-1 b) (dX/d't) + 3 (dy/dt) + 3y-0 (7 points) (d'x/d't) +3y-te' x(0) = 0 x'(0) = 2 y(0) = 0 c) An nxn matrix A is said to be skew-symmetric if AT--A. If A is a 5x5 skew-symmetric matrix, show that 9detA)-0 (4 Points) d) Suppose A is a 5x5 matrix for which (detA) =-7, what is the value of...
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5) (9 points) Graph the following conic. 9(x - 2)2 + 16(y + 1)2 = 144
5. [-/2 Points] DETAILS SCALCLS1 10.2.025. Solve the initial value problem dx/dt = Ax with x(0) = Xo. A-[3] [2] x(t)
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b. ASSUME the Differential Equation: dx dt :-(W2)x. 1. SOLVE. That is, determine a function x = f(t) which satisfies the above. 2. CHECK. Show that your function to the above dif. eg. is, indeed, a solution.
Problem 5 (10 points). Consider the function f(x) = L. (1-4e+") dt, defined in (-3, +00). Find the local max/min of f(x).
from ch8 section 3. please show all steps and write clearly
Use the methods of section 8.3 to find the general solutions of the given systems of differential equations in the following two problems. 5. = x + 3y + 1 dx dt dy dt = x - y - 1
The equation for the unforced, damped pendulum is 2 d0 -mg sin ml 2 dt which, calling 0 by x, can be written as a pair of first order ODE's dx 2 dt For Quiz 9, please submit the phase plane for equations (1) with the values -1,e1 in the ranges -8 < x < 8,-3< y < 3. 0 In particular, draw in the three trajectories passing through the points Submit the same diagrams for the undamped case e...
Problem 3. Consider the following continuous differential equation dx dt = αx − 2xy dy dt = 3xy − y 3a (5 pts): Find the steady states of the system. 3b (15 pts): Linearize the model about each of the fixed points and determine the type of stability. 3b (15 pts): Draw the phase portrait for this system, including nullclines, flow trajectories, and all fixed points. Problem 2 (25 pts): Two-dimensional linear ODEs For the following linear systems, identify the...
The equation for the unforced, damped pendulum is 2 d0 -mg sin ml 2 dt which, calling 0 by x, can be written as a pair of first order ODE's dx 2 dt For Quiz 9, please submit the phase plane for equations (1) with the values -1,e1 in the ranges -8 < x < 8,-3< y < 3. 0 In particular, draw in the three trajectories passing through the points Submit the same diagrams for the undamped case e...