Q1: Let x = [ x(t) y(t) ] and consider the system of ODEs x' =...

Q1: Let x = [ x(t) y(t) ] and consider the system of ODEs

x' = [5/2, 3; −3/4 ,−1/2] x.

(1)

1.1 Solve the initial value problem subject to x(0) = 1, y(0) = 1.

Expert Solution

Colby Messinger answered 1 year ago

Find solutions to the following ODEs: • y¨ − y˙ − 2y = t, y(0) =...

Find solutions to the following ODEs: • y¨ − y˙ − 2y = t, y(0) = 0, y˙(0) = 1 • y¨ − 2 ˙y + y = 4 sin(t), y(0) = 1, y˙(0) = 0 • y¨ = t 2 + t + 1 (find general solution only) • y¨ + 4y = t − 2 sin(2t), y(π) = 0, y˙(π) = 1

Consider a system with the input/output relationship y(t) = x(t)cos(15πt). (a) Is this system (i) linear,...

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1. Let X and Y be non-linear spaces and T : X -->Y. Prove that if ...

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Let M(x, y) be "x has sent y an e-mail message" and T(x, y) be "...

Let M(x, y) be "x has sent y an e-mail message" and T(x, y) be " x has telephoned y, " where the domain consists of all students in your class. Use quantifiers to express each of these statements. g. There is a student in your class who sent every one else in your class an email message. I answer ∃x( x ≠ y ∧ ∀? M (x, y) ) But answer on text book is ∃x( x ≠ y → ∀?...

let a be a non zero constant and consider: y''+(1/t)y'=a a. show that 1 and ln(t)...

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y''(t)+(x+y)^2y(t)=sin(xt+yt)-sin(xt-y*t), y(0)=0, y'(0)=0, x and y are real numbers

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Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}....

Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}. a) Prove or disprove: A ⊆ X b) Prove or disprove: X ⊆ A c) Prove or disprove: P(X ∪ Y ) ⊆ P(X) ∪ P(Y ) ∪ P(X ∩ Y ) d) Prove or disprove: P(X) ∪ P(Y ) ∪ P(X ∩ Y ) ⊆ P(X ∪ Y )

Let z = x2y5 , x = sin t + t3 , y = 2t2 –...

Let z = x2y5 , x = sin t + t3 , y = 2t2 – t . Find dz/dt and d2z/dt2.

Let X ~ exp(λ) MGF of X = λ/(1-t) a) What is MGF of Y =...

Let X ~ exp(λ) MGF of X = λ/(1-t) a) What is MGF of Y = 3X b) Y has a common distribution, what is the pdf of Y? c) Let X1,X2,....Xk be independent and identically distributed with Xi ~ exp(λ) and S = Σ Xi (with i = 1 below the summation symbol, and k is on top of the summation symbol). What is the MGF of S? d) S has a common distribution. What is the pdf of...

Let y(t) = (1 + t)^2 solution of the differential equation y´´ (t) + p (t) y´...

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