Solve the initial-value problem where f(t) = 2: -1; y' - y = f(t), y(0) = 1 0 ≤ t ≤1 t> 1 in the following two ways: a) Using the Laplace transform

Q: The signal x() exp(-at)u(t) is passed as the input to a system with impulse response…

A: We have given a signal ..with the help of the Fourier transform we find energy ..the procedure is…

Q: Describe in your own words the method you would use to find the Laplace transform of the first…

A: The Laplace transform of function f(t) is given by Lft=∫0∞e-stft dt and is denoted by F(s). We can…

Q: Q4 Solve step Functions in Laplace transform t < 6 x ≥ 0 f(t)= = { = 8+ (-8+ (t-6)²

A: The given problem is to find the Laplace transform of the given unit step function. Use the…

Q: Use the Laplace transform to solve the given initial-value problem. y' - 2y = 5(t – 4), y(0) = 0…

A: The solution is given as

Q: Find the cosine transform fe(w) of f(x) for f (x) = -6 if 0 2. f.(w) %3D

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Q: Let f(t) = e^t if 0=1   Write f(t) using step function and find the laplace transform. Also,…

A: We have to write f(t) using step function and find the laplace transform. Also, draw the graph.

Q: 6. Find the Laplace transform of the following functions (b) g(t) = te * sinh3t.

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Q: Use convolution and Laplace transform to evaluate y''+y=sin(t) , y(0)=1 , y'(0)=-1

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Q: Find te Inverre laplace transform of F(s) 48 2. |

A: Inverse Laplace Transform Definition: If Fs be the Laplace transform of a function ft, i.e., if…

Q: Use differentiation in time domain to solve the the Laplace transform: y"-y'-6y=0; y(0)=6, y'(0)=13

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Q: e^3(t+2)/2. Find laplace transform of the function

A: Let's find Laplace transform of given function.

Q: (6) Solve the Integro-differential equation: +4y +5 y(t) dt = e-t; y(0) = 0 dx (7) Find the Fourier…

A: Given Integro-differential equation is dydx+4y+5∫0xy(t) dt = e-t y(0)=0 The given equation can be…

Q: 6. Find the Laplace transform of the following functions (a) g(t) = et+2+ sint cost+to(t-2).

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Q: Q1) Find the Laplace transform of the following functions:- f (t) = t e-3t sin²t

A: Simplify the given function first in such a form that the formulas of Laplace transform can be…

Q: Please help me solve using the Laplace Transform y''-7y'+10y =9cos(t)+7sin(t)            y(0) = 5,…

A: solution:Given the differential equationy''-7y'+10y=9 cos t+7 sin t   y0=5, y'0=-4Taking laplace…

Q: Use the Fourier transform method to solve du k at ax2-Yu, -o∞ 0 u(x, 0) = f(x).

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Q: using laplace transform, solve the equation: y'' + 4y = 8cos(2t) - 8*exp(-2t)              y(0) =…

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Q: 5. Find the inverse Laplace transform of the function H(s) = as + b (s-a)² +32° a = 9,b= 10, a = 4,8…

A: We have to find the inverse Laplace transform of the function H(t)=as+b(s-α)2+β2 when a=9, b=10,…

Q: Use (8), • S* f(1) dt = £^¹{F(5)}, to evaluate the given inverse transform. (Write your answer as a…

A: we know that laplace transform of e^(at) is (1/(s-a)).

Q: When the Laplace transform is used to solve the IVP: y' +5 y=314, y(0) = 2 1/4+ the following…

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Q: Find the Fourier transform F(@) = | f(t)exp(iwt)dt of the function 0, t 0. You might want to use…

A: The given function is ft=0t&lt;01βtt≥0, where β&gt;0. We know that the Fourier transform of a…

Q: (a) Consider the continuous function f(t)=sin(2rnt). i) What is the period of fſt)? ii) What is the…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: Use the Laplace transform method to solve the IVP y" (t) + 3y' (t) + 2y(t) = e-³tu₂(t), y(0) = 2,…

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Q: Suppose solving an equation by Laplace transform results in 9 s Y(s) = s2 + 49' Evaluate y(0).

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Q: Solve Using the Laplace Transform c) y + 2y' + y = 8(t-1), y(0) = 0, y '(0)=0

A: Given: y"+2y'+y=δt-1; y0=0; y'0=0To find: The solution of the given differential equation using the…

Q: 8. Let 0 0 Use the definition of Laplace transform to find L{f(t)}.

A: