6. Suppose you are working out the Laplace transform of f(t) = e'+4t using the definition of the Laplace transform. For what values of s is this defined? Explain.

Q: 2. Soru Which of the following inverse Laplace transform is TRUE ?

A:

Q: xn-1 ax

A:

Q: Solve the laplace transform of f(t) = sin3 (10t). Hint: You may convert the given to whichever form…

A:

Q: (3) Solve the initial value problem using Laplace transform. y + 4y sin 3t, y(0) = 5.

A:

Q: Solve the problem: y "- 4y=excosx ,   y (0) = 1, y '(0) = 2 a) without using Laplace transform; b)…

A: Consider the given information. (a) Use the undetermined coefficient to solve the equation. Write…

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: What is the Laplace transform of y’’ – 6y’ + 15y = 2 sin (3t), with y(0) = -1 and y’(0) = 4

A:

Q: Find the Fourier transform of S (x) =!-\,| sin x dx Hence evaluate

A: Given,    f(x)= 1-x, x≤10        , x>1

Q: Q1\ Find the Z-transform of A) cosh 2

A: The given question can be solved as shown in step2.

Q: Solve the equation dy y ху-з dx II +

A: The given equation is of the bernoulli's equation form.

Q: The general solution of the initial value problem given below is the "Laplace Transform". find using

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: For given function f(t) = 2sin(3t) – 3 cosh(2f)+e6t +5 Laplace transform of L(f(t)) and L(1¶ O), dt…

A:

Q: Solve for the Laplace transform of f(t) = 5 using long method. %3D

A:

Q: 3) x(t) te-at 1 4) x(s) = (Sta)2

A:

Q: 2 The inverse Laplace transform by using integral of transform s(s2 +2s+4)

A:

Q: 2) There is a function F (s) with "different true root state". Make the inverse laplace transform of…

A:

Q: 7. Given that the Laplace transform of te is F(s) =- (s + k) Laplace transform of te" without using…

A: The solution is given as

Q: 4. Solve for Laplace transform of f(t) = t^5 using long method

A: This question is based on Laplace transform formula.

Q: 10) Use the Laplace transform to solve the given initial-value problem. y'-y = 2 cos (3t) when y(0)…

A:

Q: Solve the following initial value problems by Laplace transform technique

A: We have given a differential equation ,  y'' + 2y' + 5y = 50t - 100   ,  y2 = -4  , y'2 = 14 This is…

Q: What is the Laplace transform of (1 + e4t)?

A:

Q: 1 If the Laplace transform of ewt is , the Laplace transform of t coshtis S-W

A:

Q: Suppose solving an equation by Laplace transform results in 6 s Y(s) = s² + 64° Evaluate y(").

A: y(s)=ℒ(6ss2+64) =-3(2si(8s)-π)sin(8s)-6cos(8s)ci(8s) y(π)=-3(2si(8π)-π)-6cos(8π)si(8π)

Q: 2)

A:

Q: How is the existence of the Laplace transform of a function guaranteed?

A: We known that the  Existence of the Laplace transform of a function guaranteed

Q: 5. Use Laplace transform technique to solve , y"-y'-6y = 0, Given y(0) =1 and y'(0) = -1

A:

Q: x(t)=sin(t-3T)

A: Z transform

Q: Consider the IVP: y" - y' + 2y = 8sin(2t) - 8, with y(0) = -2, y'(0) = -4. Solve the IVP by using…

A: Given IVP is y''-y'+2y=8sin2t-8              (i) With y0=-2, y'0=-4 Taking Laplace transformation of…

Q: Determine the causal signal x(n) if its z-transform is given by 1+2₂-2 1+z=2

A:

Q: Find Lf" sin /6t-r'e"}

A: Please see below

Q: 1. Show that the function 2t et cos (et“) is not of exponential order, however its Laplace transform

A:

Q: Solve the laplace transform of f(t) = sin (10t). Hint: You may convert the given to whichever form…

A:

Q: welą Find the inverse Laplace transform of ,-7s F(8): s2 – 1s – 6 f(t) = - (Use step(t-c) for u,

A:

Q: 25. а. Apply Fourier transform to solve: ди for 0 < x, t 20 Under the conditions,

A: Given,              ∂u∂t=∂2u∂x2,  for  0≤x, t≥0           (1)Under the conditions,…

Q: [a² - x², Find the Fourier transform of f(x)= • 0, and hence 1C. |x| > a evaluate (Sin sint-t cost…

A:

Q: ) Solve the following initial value problem by using Laplace transform. y" + 4y = 4t + 12, y(0) = 4,…

A:

Q: Show that (a) L-1 = sin(at) - tcos(at) %3D (s²+a²)²) (where L indicates imverse Laplace transform)…

A: L-11s2+a22=12a2sin(at)-12a2tcos(at)

Q: Find laplace transform of x" + 3x' + 2x = t(e^(-t)) Where x'(0) = 0 , x(0) = 1

A:

Q: What is the inverse Laplace transform of Y (s) = (4s + 4)/ (s2 + 4s + 13)

A:

Q: 2s+4 What is the value of the inverse Laplace transform given byL 82 +2s + 3

A:

Q: 1. Prove the scale change theorem on the Laplace transform, that L[f9) = aF (as)

A:

Q: How is the Laplace Transform defined? What is its notation?

A: Laplace transform of the function f(t) is defined by   ∫0∞f(t)e-stdt

Q: 27. Explain why this function does or does not have a Fourier transform. If it does, compute its…

A: The given function: f(x)=0,             |x|&gt;1excosx,   |x|&lt;1 This function have a Fourier…

Q: Can you provide 2 Examples of Finding Laplace Transform containing t and exponential using the…

A:

Q: 1: A :Find Laplace Transform of f(t) = sin²t By Rule.

A:

Q: Use the Laplace transform to solve the initial value problem: (Please write clearly so i can follow…

A:

Q: Solve differential egualions by using laplace transform fCW)-5)'(x)+6f(x)=0 where for-o and flo)=1.

A:

Q: 4. Use Laplace transform technique to solve , y"+2y'+2y = e given y(0) = -2 and y'(0) =-1 %3D

A:

Q: 4. Use Laplace transform technique to solve, y"+2y'+y=4e given y(0) = 2 and y'(0) = -1

A: We have to find general solution of given differential equation using Laplace transform Method.