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: 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: using con |' 1 P+ (1)

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

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

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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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