d. 9 – 12 + 4y = 121e-", y(0) = 10, y'(0) = 6 dt2 e. + + 4y = 8t – 10, y(0) = 1, y'(0) = 7 d'y dy dy f. 3 – 2 - y = 2y – 1, y(0) = 7, y'(0) = 2 dt

Q: = Find the inverse Laplace transform f(t) = L-¹ {F(s)} of the function F(s) = f(t)= [38+4 +36 = L-1,…

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Q: -7 s(s+3) 2

A: Given: L-1-7SS+72

Q: ∞ -3t Evaluate test sin 3t dt. [Hint: Use the definition of Laplace transform]

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Q: 4. Find L'{ -}. Give table number. 3-5S

A: We have to find L-123-5swe are going to use the formulaL-11s-a=eat ——(*)

Q: Show that the Fourier transform of f (x)= e*/2 is e

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Q: Use the Laplace transform to solve the difference equation 3x(t) — 4x(t − 1) = 1, x(t)=0 for t < 0.

A: Given: The difference equation, 3xt-4xt-1=1, xt=0 for t&lt;0   To solve: The given difference…

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Q: h(t)=t^2sin(3t) laplace transform

A: Given function is,                h(t) = t2 sin3t (.)  Some properties of Laplace transform :- (i)…

Q: Find the Fourier Cosine Transform of the function -mx f(x) = (ae-m +be¯¹x}³_if_x>0 if a = 5, b = 4,…

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Q: Find the Fourier transform of f(x) and show details f(x) = {x²² 18 -1<x<0 otherwise

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Q: find the fourier transform of logx u(t)

A: Unit step function: u(t)=1t≥00t&lt;0 Fourier transform of a function fx is  Fp=∫-∞∞fteiptdt…

Q: Derive the Fourier transform for f(t) = te2t for t>0 and 0 for t<0.

A: The Fourier transform of the function f(t) is represented as F(k), it is defined as ∫-∞∞e-iktf(t)dt,…

Q: Find the Fourier transform

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

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Q: 7) f(x)= xe-x 0 if -1<x<0 otherwise

A: Formula for the Fourier Transform of fx is  Fw=∫-∞∞fxeiwxdx  We are given fx=xe-xif…

Q: to at

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Q: Find the function f(x) that has Fourier transform (k) = (1+k4)-1.

A: Here we have to find out  .Now from definition of inverse fourier transform , to evaluate this…

Q: Obtain the Fourier transform of the function where f(x) = 0 for x &lt; 0 and f(x) = e−axsin(bx) for…

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Q: Find Inverse Laplace transform of this -{in (1 + #)}' where c is a constant.

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Q: -Obtain the Fourier transform of f(t): = sin (30) -t²+7it+12

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Q: Determine the Fourier transform and plot the magnitude S1, It| < T/2 l0, otherwise (ii) x(t) = f(x)…

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Q: f(x) = 0 if -1<x otherwi

A: Formula for the Fourier Transform of fx is  Fw=∫-∞∞fxeiwxdx We are given fx=|x|if…

Q: Q6/ Find the Inverse Laplace Transform 4-L-1( s-3 )

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Q: Find the Fourier transform $\tilde{f}(p)$ of the function 4x²e-5¹ for x ≥ 0 for x < 0. f(x) = {…

A: fx=4x2e-5xfor x≥00for x&lt;0

Q: Use formulas from this course to find the inverse Laplace transform (a) L-1{+1) 2s+1 1 252+8 (b)…

A: Solution:

Q: Use Laplace transform technique to solve y+2y+2y=e, y(0) = 3, y (0)=-3

A: We need to use Laplace transform to solve this differential equation.

Q: Compute the Fourier transform of the Heaviside function

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Q: 50° S. 80° R 60° 100 7. 7.

A: The measure of the arc length is double than the angle formed by that arc to the circumference of…

Q: F(s) 8Bs - 7C (s + 3)(s - 4) (As − 1)

A:

Q: Find the Fourier Transform of f(s) = e-ax= a >0

A: The Fourier transform of a function  is given by :

Q: Find the inverse Laplace transform. F(s) = 1/s - 2/s^5/2

A: This question related to inverse laplace transform.

Q: find

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Q: sx 14-X Find the Fourier transform of function f(x) = , 0<x< 14 14 < X <16

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Q: Find the Laplace Transform 3 1- f(t) = 3t4 – 2 ti+ 6

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