Q.6: A process X(t) with Cxx (t, t+t) = E(X² (t)) - cos(T). We have E(X(t)) =A) ±1B) 1C)+2D) 3E) NoneQK3

We have E(X2(t)) = cos(T) By the definition of variance, we have that Var(X(t)) = E(X2(t)) -…

Answered: Q.6: A process X(t) with Cxx (t, t+t) =…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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1) Consider the second-order equation where A x (t) = Ax(t), -3.2 5 -2 2.8 Suppose that the initial condition is to := x(0)= (1,0) e R2. Let t₁ be the smallest t> 0 such that r(t) = (x₁,0) for some x₁ > 0. Compute x₁.
If z=1+y , I= e cos(s) and y=e' sin(s), then at (t, s) = (1,0) is as O-2e O 2e2 O 2e
b) Use Laplace transform to solve the system of differential equations UTM &UTM UTM dz - I = 4y, dt dy given that at t = 0, x = 3, and y = 0. dt IM UTM UTMUTM 6UT TM
2022 Use appropriate techniques to solve 1) 1 xe2t+ dx dt dx dt || · 1 11 2t+x.
Q1.2 a find the biggest interval on which theorem 3.1.1 guarantees that the initial value problem has a unique 1 (x + 5) y" + (x³²-4) y² + 17y= 2² +1² 460) = 3₂ y ₁ (0) = 69 4" (0)=6 ' x +I³ options a) (-∞, -1) e) (-5,1) i) (-1,5) answer var. problem has b find the biggest interval on which rantees that the g unique (۱ - ره-)(e following solution. i)(-5, ∞0) b) (0,5) f) (-∞, -5) j) (-5, -1) 1) (1,5) Note: c) (-∞0, 1) g) (1, -∞) 1 (x - 57y" + (x²-4)y" + 17y = = = = = 54(0) = 3₂ y'(0) = 6+y" (01=6 + 1 Answer Options a) (-∞0,1) b) (1,00) f)(1,5) j) (-1,5) d) (5,00) 4) (5, ∞0) 4) (-1,00) theorem 3.1.1 following initial value solution. c)(5,1) 9) (-1,00) K) (-∞,5) d) (5,∞0) W)(-∞,-5) 2)(-5, -1) Theorem 3.1.1 Existence of a Unique Solution Let an(x), an-1(x), ..., a₁(x), a (x), and g(x) be continuous on an interval I, and let a,(x) = 0 for every x in this interval. If x= xo is any point in this interval, then a solution y(x) of the initial-value problem (1) exists on the interval and is…
let z
4. Find a particular solution of x' = [ +1 ]] = + [8 sin ³]. sint]. Hint: xp = x(t) [X-¹(t)f(t) dt is a particular solution of a' = Ax + f.
3. f (t) -3n -2n 2n 3n f(t) is a periodic function and express f(t) in the form f(t) = ao + En=1( ancos (nwot) + bn sin(nwot))
1. Find Dr(t) and D²r(t) if (1) r(t)=(3t-4)³i+e¹j+k (2) r(t) = sin² ti+cos3tj+t²k 2. If r(t)=√t-li+ln(21²)j and h(t)=e³¹, find D, [h(t)r(t)].

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Q.6: A process X(t) with Cxx (t, t+t) = E(X² (t)) - cos(T). We have E(X(t)) = A) +1 B) 1 C)+2 D) 3 E) None