Question 3 Consider the following deterministic ODE describing the harmonic oscillator problem 3.1 Show that 3.2 Now consider (3) perturbed by noise dX = Ydt, dY == -Xdt. :(X² (t) + Y²(t)) = 0 (x² (t) + (3a) (3b) dX = Ydt dYXdtydW (4a) (4b) where W(t), is a one dimensional Brownian motion. Show using Ito's formula that the following ODE holds for the average energy of the system E(t) = E(X²(t) + Y²(t)) dE(t) dt (5)

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ky and k is a nonzero constant, then y could be (A) 2e*y (B) 2e (B) (C) e+3 (D) kty+5 2. OD OB ョ0 O A Question 2 = cos(2x), then y= %3D (A) 2. cos (2x)+C (B) 2. cos (2x) +C (C) 극sin (2x)+C 2. D) 극 1. sin2 (2x)+C 1. (E) --sin (2x)+C 2. 2.

powered by desmos Question 28 dy What is if the function y = f(x) is implicitly defined by the equation 5x + 3y² = 4y + 2x² - 5? dx O4x5 бу - 4 O4x1 by O4x +9 by O4 - 10 бу - 4 -15- < Previous

I need an answer as soon as possible, please use the class method

If y = f(x) in the figure, find the following. y 1 -6 −4 -2 (a) f(9) = (b) f(5) = 12 10 8 6 4 2 -4 (5, 6) 2 4 (2,2) (9, 10) L CO 8 +X 10 12

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Question 21 Given the function f (x,y) = x³ - 5x² + 4xy-y2-16x - 10. Which ONE of the following statements is TRUE? OA (8.16)

Write a plot of a Gaussian function with x-axis range from -3 to +3 and y-axis range from 0 to 1.2

10. [Motion in R³] A drone has an initial position of (3,1,2) and an initial velocity of (-2,5,1). The drone's acceleration can be given by the function a(t) = (4 - 6t, 9 sin(3t), 10e-2t). (a) Derive a formula for the position of the drone as a function of t. (b) If the drone flies for 4 seconds, where does the drone end up?