b) The output response y, of a discrete time system is given by Yn = 2 xn + 0.55 yn-1 – 0.1 yn-2 iii) Calculate the first 5 steps (from 0 to 4) in the response to a unit impulse input, assuming the initial internal state of the system is zero.

Q: 4) Compute and sketch the output y(t) of the continuous-time LTI system with impulse response h(t) =…

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Q: 4 3. Apply Euler-Maruyama method as one step to solve the SDE dy = 3/dt+dB₁ 5-1 y(1) = 2

A: Given that the SDE is dy=3-y5-tdt+dBty1=2

Q: 3) The impulse response of a certain linear system is h(t) = u(t) + d(t). Determine the zero state…

A: The zero state response for t≥0 is:  yt=ht*ute-t      =ut+δt*ute-t      =∫-∞∞uτ+δτut-τe-t-τdτ…

Q: • Exercise 4. Solve the initial value problem Y' = AY, Y(0) = Y, by computing etAY, where (2 1 1…

A: Given A=211110101,Y0=11-1. solve the IVP.

Q: Find the elgenpairs of matrix A and the vector Kty such that the initial vahue problem * = Ax, x(0)…

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Q: 2. (a) Why do you need Monte Carlo integration? (b) Generate 5 random values from uniform (0,1)…

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Q: transform the given initial value problem into an initial value problem for two first-order…

A: Consider the given second order IVP u′′+0.25u′+4u=2 cos(3t), u(0)=1, u′(0)=−2.

Q: .The system x′=3(x+y−13x3−k),y′=−13(x+0.8y−0.7)x′=3(x+y−13x3−k),y′=−13(x+0.8y−0.7) is a special…

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Q: 5. Consider the system of differential equations dx 3r – 2y %3D dt dy 2x + 3y dt a. Find the general…

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Q: Suppose that the damping effect of the system is changed (b-10). How will this affect the response…

A: As per the question we are given a mass-spring-damping system as : mass m = 1 spring constant k = 6…

Q: 5.6 Find a state-feedback control law u so as to minimize | (x² + u?) dt J 0. subject to i = -x + u,…

A: The function for state feedback control is J=∫01x2+u2dt The value of x¯is -x+u and x(0) is 2.

Q: An LTI system has impulse response h(t) = (1/t“) u(t – 1). Show that the system is BIB0 stable if a…

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Q: Q1) The impulse response of a linear time-invariant system is: h(n) [1 0 -1 3-2 4-2], Determine the…

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Q: Consider the IVP +20² dt² dx dt 4t- + 4x = 0, with x(1) = 0 and x' (1) = -3. Show that x₁(t) = t and…

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Q: find the critical points for dA=2A=0.01 AL and dL/dt=-0.5L+0.0001AL

A: Critical points are the points in a graph, at which the direction of graph changes.

Q: (a) Find a second-order homogeneous linear ODE for which the given functions are solutions. (b) Show…

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Q: How do you solve this problem?

A: We are given the system of differential equation,                          . We are also given the…

Q: Consider the initial value problem i = Ar with a(0) = 2o € R where 1. = T0 %3D -1 0 0 A = 0 10 0 1 1…

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Q: 7. Apply the Gauss-Seidel method to Exercise 3.

A: Consider the system of linear equations, 2x1-x2=2x1-3x2+x3=-2-x1+x2-3x3=-6 The objective is to solve…

Q: linear algebra

A: To determine all solutions of the given linear system of differential equations in two unknowns,…

Q: Convert the differential equation x''' = x'' – 2x' – 4x +t into a system of first order equations by…

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Q: 2. Determine the expressions for the unit step response for the systems represented by the following…

A: 2) ii  Given,X0sxis=10s2+65+5Given , unit step responsexis=1/sX0s =10ss2+65+5X0s =10ss+1s+5using…

Q: How do you solve this problem?

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Q: Consider the initial value problem of a system of linear differential equations x' = Ax+eAt "A], =…

A: The Given Initial value problem is: x'=Ax+eAt01 , x(0)=10, Where A is 2×2 Constant matrix. Let…

Q: the given system of differential equations to a first-order linear system. dx/dt  - ty  =  cost…

A: We have to change given system in first order system: Given system is:

Q: 14.8. It has been suggested that the short-term interest rate r follows the stochastic process dr =…

A: Given Information: Consider the rate r follows the stochastic process which is defined as:…

Q: Consider the initial value problem of a system of linear differential equations x² = Az + et [H],…

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Q: 02/ The following system of equations is designed to determine concentrations (the c's in g/m²) in a…

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Q: 1 c) Does there exist x0 such that y = 1 is a steady state of the system xk+1 = Axk starting from…

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Q: b) Let = .5P – 50. Find the equilibrium solution for P. Furthermore, determine whether P is dt…

A: To find the equilibrium solution for P

Q: Solve the initial-value problem dx -2x – 2y dt dy -2x + y, dt where the initial condition (x(0),…

A: I have Transferred into a matrix differential equation and then solved

Q: Find a particular solution satisfying the given initial condi- tions. 13. y(3) + 2y" – y' – 2y = 0;…

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Q: (t -x)dt – tdx =0; when t = 1, x = 5

A:

Q: Consider the initial value problem = , where -0 0. If u(x,0) = 2 and u (x, 0) = x + 5, then u(x, t)…

A: This is a wave problem and can be solved using D'Alambert's formula:…

Q: Q2/ Show whether that there is a solution to the system by using Jacobi's mehtod when the initial…

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Q: Solve the initial value problem for the linear system in dimension 3: 3 1 x'(t) = 9 -1 x(t) 4 -1…

A: First we find the eigenvalues and corresponding eigenvectors for the matrix A, then we find the…

Q: Find the total solution and state transition matrix for the system d [x(1 dt Lx2(t) -1 %3D with…

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Q: Find a particular solution satisfying the given initial condi- tions. 14. у3) — 6у" + 11y'- бу %3D…

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Q: 10

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Q: Transform the given initial value problem into an initial value problem for two order equations. u"…

A: The second order differential equation can be transformed in two first order differential equation…

Q: 1. Consider the following linear systems of ordinary differential equations: (a) dx/dt = 3x – 2y,…

A: Since you have posted a multiple question ,I will solve the first question  for you. To get…

Q: Q2/ Show whether that there is a solution to the system by using Jacobi's mehtod when the initial…

A: To start Jacobi method, the set of equations:…

Q: 1. A system is modeled by using the equation, *+3x+3x=0; and the initial conditions are given by…

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Q: 2. Write the system of differential equations dar - 2r+y. dt du <-5a-2y dt in a matrix form, compute…

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Q: Solve the initial value problem for the linear system in dimension 3: 3 1 x' (t) = 9 -1 x(t) 4 -1…

A: To solve the given initial value problem, first we find the eigenvalues and corresponding…

Q: 9

A:

Q: (c) Identify the unit impulse response of an Linear Time Invariant Continuous system specified by…

A: Given: (D2+6D+9)y(t)=(2D2+9)x(t)

Q: Determine the largest interval (a,b) for which the existence of a unique solution using Theorem 1 in…

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Q: a) Show that the fourth-order Runge-Kutta method, k₁ = hf (ti, wi), h k₁ k₂= hfti+ Wi + 1/12) 2' h…

A: Given:  k1=hfti, wik2=hfti+h2, wi+k12k3=hfti+h2, wi+k22k4=hfti+h, wi+k3 and wi+1=wi+16k1+2k2+2k3+k4…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.