Use the Laplace transform (a) x' — 5x = e-2t, Isitne Joh auto (b) x' + 3x = 3t+7, x(0) = 1 (c) x" + 3x + 2x = 12e¹, x(0) = 2, (d) r" - 4x = t, to solve the initial value problem x(0) = 3 on 700 x'(0) = 3 x(0) = 1, x'(0) = 2.

Q: 1. f(t) = 5(e^-4t)[cos(10t)] A. (5s – 20) / (s^2 - 8s + 116) B. (s - 4) / (s^2 - 8s + 116) C. 50 /…

A: Laplace transferom of the function

Q: 4s 4 2-¹ (1-16) - O (5/2) e^(-4t)+(3/2) e^2t O None of them O (5/2) e^(-4t)+(3/2) e^4t (5/2)…

A: The given inverse Laplace transform .We have to find the inverse Laplace transform.

Q: Problem 5 Using Laplace transform, solve y" - 4y + 7y = 0 y(0) = 3, y'(0) = 7

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Q: Use the Laplace transform to solve the given initial-value problem. y" +9y' = 8(t− 1), y(0) = 0,…

A: The initial value problemFrom the Laplace transformFrom the initial values

Q: Solve the given initial-value problem using the Laplace transform: -{- = x(0) = 5. x' + 3x if 0<t<4…

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Q: Laplace Transform. Please show your complete solution

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Q: Yn+2-6yn+1 + 8y₁ = 3n²+2-5.3n Solve the following using Z-Transform, when y(0)=0 and y(1)=1.

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Q: Solve by Laplace transform method x' = 2x – 2y у'3 х — у — cos t x(0) =,y(0) = 3 4

A: Solution: The system is x'=2x-2y y'=x-y-cost x0=35,  y0=45

Q: 8.(a) Find the Fourier transform for the function cos x, -n/2 7/2 f(x) = 0, (b) Use the result in…

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Q: Show that d(w) - = [6(w− 1) + 6(w+1)] is the Fourier transform of cos(t). Show that d(w) = −ix[8(w −…

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Q: 2e 5(s+1) (a) Determine I |(s+4)' ` s² +2s +5 3.

A: As per the company's guidelines, we are supposed to solve the first question for you, kindly repost…

Q: 3. f(t) = [sin(2t)]^2 %3D

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Q: The Laplace transform L{e^-t^2} exists (because it is exponential order), but without finding it…

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Q: Find the inverse laplace transform of the followings; a)  X(s)=(s+2)/(s^2+2s+5)…

A: a) Xs=s+2s2+2s+5 Apply Laplace Inverse transform…

Q: Confirm that the standard Fourier forward transform of the double-sided decaying exponential signal…

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Q: Chapter 4] If f(x) = dt, where g(x) = 1," (÷) V1+t3 [1 + sin(t²)] dt, find f'

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Q: 2. f(t) = -7(e^3t)[sinh(2t)] A. -14 / (s^2 – 6s + 5) B. (-7s + 21) / (s^2 – 6s + 5) C. -14 / (s^2 -…

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Q: Laplace transform of x(t) = cos(4f)u(t) %3D 16 X (s) = s* +16 4 X (s) = s* +16 X(s)D s? +4 X(s) = s´…

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Q: 1.X" to qx' +5x, = 5ot x'l6) :: -5 , x6) - 5

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Q: F{6f"(x) – 2f' (x) + 7f(x)} =

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Q: 2x" - 3x' + x = 0 x(0) = 2, x'(0) = −1

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Q: 1. Deduce the continuous function whose Laplace Transform is 10 F(p) P (p² + 9) 2.Find Р2—ЗР+10 (i)…

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Q: c) Find f(-1) if f(0) = 2, f(1) = 9, f(2) = 28, f(3) = 65, f(4) = 126, f(5) = 217. %3D

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Q: the Inverse Fourier Transform x(t) of each signal X(w) given below. X(w) = -4 sinc² X(w) = πd(w − 1)…

A: "Since you have posted multiple questions, we will provide the solution only to the specified sub…

Q: Given that the Fourier transform of e- πt^2 is e- πs what is the Fourier transform of the following…

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Q: What is the Fourier transform of 8(x) dx F(k) = 100 = 2T -ikx 8(x) =?

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

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: Suppose solving an equation by Laplace transform results in 4 (s+ 18) Y (s) : %3D (s+9)² * Evaluate…

A: Laplace transform of the function y(t) is defined as Y(s)=∫0∞e-sty(t)dt, where s&gt;0. Since the…

Q: Give the Inverse Laplace Transform of s/((s+2)(s^2+4)). * O -1 + (e^(2t))cos(3t) O t+ (9/4)e^(-2t) -…

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Q: Suppose the Fourier transform F(w)=re-lwl, is known. Show that the inverse Fourier transform, viz.,…

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Q: The inverse Laplace transform of F(s) = = -98 e 8² +18 2 is

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Q: 5. Find the general solution to x₁ = 4x₁ + 2x₂ + 3et, x₂ = 2x₁ + x₂ + et using Laplace transform.

A: The given system of differential equation is  x1'=4x1+2x2+3etx2'=2x1+x2+et To find the general…

Q: x+L. -L <x< 0, |L, f(x) = f (x+ 2L) = f (x) Problem 2: 0 < x < L;

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Q: Find the Laplace transform, 0 0st<5 g (t) = { (t-5)² t25 O e^-5s/s^3 O (2e^-5s)/s^3 O (2e^-5s)/s^2 O…

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