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: The impulse response of a DT system is h[n] = 3^(n-1)u[n] . Calculate the input x[n] which generates…

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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…

Q: 4] Find the Laplace Transform of f(t) = { S-1 (-/= + 5 = /₁1) (1te - 1/₁1) (a) (c) S S - I (b) (d) S…

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Q: Solve using Laplace transform y"-2y' +5y=1+t, y(0)=0, y'(0)=4

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Q: 5. The following linear differential equation models the charge on the capacitor, q(t), at time t in…

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Q: B/Fnd Z transform z(n) = " (n) – u(n-5))

A: Given equation: x(n)=15nun-un-5

Q: using con |' 1 P+ (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: Use the laplace transform to solve 3x'-y=2r;x'+y'-y=0; x(0)=y(0)=0

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Q: Consider the polynomial f(x)=5x-2-5x2. Using the forward divided difference approximation for the…

A: Given polynomial function is  fx=5x−2−5x2 To determine the step size and approximation of the first…

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: The Laplace transform of x(t) is X(s). Given x(0)=2 and x'(0)=-1, write an expression for the…

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Q: By using convolution theorem for Laplace transform, prove that 1 L-1 + x}={erf (2√x) PVp +4

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

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

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Q: %3D Apply the Chain Rule to find the tangent line to f(x) = 4v2x- 6e2-*at x = 2

A: We want to find the tangent of the given function at x=2 We know that slope of the tangent at a…

Q: Use differentiation in time domain to solve the the Laplace transform: y"+7y'+12y=21e³t; y(0)=7/2,…

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Q: In each of Problem, write the Fourier integral representation (14.1) of the function and determine…

A: The Fourier integral representation of a function f(x) is given by:   f(x) = (1/√(2π)) ∫[from -∞ to…

Q: Use the laplace transform to solve 3r'-y=21;x'+y'-y=0; x(0)=y(0)=0

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Q: Find the inverse Laplace transform f(t) = £¯¹ {F(s)} of the function F(s) = e −3s (1 – 4s) s² + 16

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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: d the Laplace transform F(s) of f(t) = 5tu(t – 4) F(s) = (5/s^2+10/s)e^(-5s)

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Q: Let f(x) = In(x² – 14x + 52) f'(x) =

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

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