Use Laplace transforms to solve the integral equation y(t) – 3 y(t – v) dv = -e 4t The first step is to apply the Laplace transform and solve for Y(s) = L(y(t)) Y(s) = Next apply the inverse Laplace transform to obtain y(t) y(t)

Q: 00 1. Find the laplace transform of, f(t) =sin(t +a)cos(t -a) using e-stf(t)dt.

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Q: f (t) = 2e¬ + 4 sin t cos t %3D

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Q: A function f(t) is defined by f(t) = 4 0<t <3 = 2t + 1 3 ≤t. Sketch the graph of the function and…

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Q: Laplace transform L{k(t)} = -5{L(t2e-4t)}+L{sin(3t)}

A: We need to find the Laplace transform of the above.                       L{k(t)} =…

Q: Find the Fourier transform of the function f(t) = e-2. 2. ii. Using Fourier transforms prop erties…

A: The Fourier transform of the function is represented as , it is defined as , where . Since the…

Q: Find the Fourier transform of each function. In each case, a is a positive real constant. Answer:…

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Q: Use Laplace Transform to solve Ø(t) + 2 * cos(t−7)ø(7)dt = e¯¹ for ø(t). -t 0

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Q: f(d) = e-2d d4

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Q: (a) Find the Laplace transform of the function: f(t) =e-$' t3/2 (b) Find the Laplace transform of…

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Q: (b) Given f(t) = sinh(-4t)U(t – Jand g(t) = sinh(-4t) * U(t – ) where U(t – a) is the unit step…

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Q: Do the Laplace transform of x(t) x(t) = (t + 1)²e¹u(t) + e-3t cos (t) u(t)

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Q: Find the Laplace transform F(s), given that f(t) is: (a) 2tu(t – 4) (b) 5 cos(t) 8(t – 2)

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Q: Let x(t)=5sinc(1.5t) +6cos(7/2) and h(t)=4sind(). Determine y(t)=x(t)*h(t) using Fourier Transform…

A: Let  and We need to determine y(t)=x(t)∗h(t).To solve this problem, we list the Fourier transforms…

Q: Compute the Laplace transform. Your answer should be a function of the variable s L{3+ u(t)e sin(7…

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Q: (b) Find the Laplace transform of f(t) = t + te (i) First solve using integration Then solve using…

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Q: (e²t) LE9+² +6t+73 L{ 5 cos (4+) } -4t L {ett sin (8t) 3

A: Given that the Laplace functions Le2tL9t2+6t+7L5cos4tLe-4tsin8t .

Q: Solve the laplace transform 3x-6x= Sin 2t %3D given when t=0

A: Use the laplace transformation table and derivative formula

Q: 1 Find the Fourier sine and cosine transform of ƒ(x)=

A: Use the Fourier Sine and Cosine transform table to obtain the result.

Q: (b) Given f(t) = sinh(-4t)U(t – -)and g(t) = sinh(-4t) + U(t - -) where U(t – a) is the unit step…

A: The unit step function or Heaviside's unit step function Definition: The unit step function is…

Q: 4.0 f(t) = 3 – e-3t + 5 sin 2t

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Q: . Let g be the piecewise linear function g(t) = (t-5), t = [0,5) te [5, 10) t> 10. Express g using…

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Q: Find the Fourier transform specified in part (a) and then use it to answer part (b). (a) Find the…

A: In part (a) we have to find the Fourier transformation, Given, f(γ,p,t)=e-γtsin pt  t&gt;0,0…

Q: Find the inverse Laplace transform of f(t) F(s) = = help (formulas) (Notation: write u(t-c) for the…

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Q: orm y(t) = 4e-2cos

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Q: Find the Laplace transform of the given function; a and b are real constants. f(t) = e** sinh(bt)…

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Q: Solve the Laplace transform of: 3 cos 8t + 2 sin 8t

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Q: %3D b)ë + 4x = t,x(0) = 1,x(0) = 0 %3D

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Q: 3.0 f(t) 2e-104 +t+5e 1)(t +5) 4.0 f(t) (t- 5.0 f(t) = t² -7+ sin 2t %3D %3D B.Find the I

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Q: Find: x - 4x + 13x = 2 sint, x (0) = 1, x(0) = 0 (a) Obtain the solution to the ODE by solving for…

A: Solution of the differential equations using Lapalce transfermation and homogeneous method

Q: Find a function f(x) whose Laplace transform is e-3p p² +25 You should find f(x) = K sin(R(x -…

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Q: x2, Ixl a

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