Take the Laplace transform of the following initial value and solve for Y(s) = L{y(t)}: y" +9y= = (sin(#t), 0

Q: f(t) = sinhtcost

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Q: Use the definition of the Laplace transform to find L{cos(at)} where a is a constant. You must use…

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Q: Solve for the laplace transform x(t)= (cosh4t sin4t)/ (te6t)

A: The given function is x(t)=cosh 4t sin 4tt e6t=cosh 4t sin 4tte-6t

Q: Consider the following ODE y' = y+t/y+1 Which kind of ODE is ?

A: Given ODE is y'=y+ty+1. Simplify y'=y+ty+1. ⇒dydt=y+ty+1⇒y+1dydt=y+t⇒y+1dydt−y=t..........1 Since,…

Q: Q1: Find Laplace transform for the following functions 4) f(t)=t sinh(at)

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Q: 3. Suppose y(t) is the inverse Laplace transform of the following function: y(t) = L-1 What is lim…

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

Q: 7. Evaluate y" + y' = t; y(0) = 1 , y'(0) = -2

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Q: f (t) = e(-3t) sin(2t) cos(3t) cosh(t)

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Q: If F(s) = -3s² s + 1 is the Laplace transform of f(t), find the following, correct to three decimal…

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Q: If the percent decrease is 25%, what is the common ratio?

A: Common Ratio The common ratio is defined as the amount between each number in a geometric sequence.…

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

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

Q: 7. Obtain the Fourier sine transform of the following functions: sin wx (c) x² +1' w > 0

A: The given problem is to find the Fourier sine transform of the given function, we have a general…

Q: Find the Laplace transform F(s)=L{f(t)} of the function f(t)=e^(−3t) cosh⁡(5t).

A: Laplace transform of the function, f(t)=cosh(at) is

Q: 3) Determine the inverse Laplace Transform. where f = L{F}. 4 F(s) = In s- 3, %3D

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

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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: g (t) = tsin (nt)

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Q: Using convolution property of Laplace Transform, solve for y(t) of the following: 2) y(t) = sin(nt)…

A: The given problem is to solve for y(t) for the given function by using convolution property of…

Q: The Fourier Cosine transform of the function f(X) = {1, |x| a} a A 1/(/2n)*(cos(as)/s) B…

A: Given functionfx=1,x<a0,x<aFourier cosine transform of f(x) is given byFcfx2=2π ∫0∞ f(x)…

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: 4. Using the definition, not the table, find the Laplace transform of (a) f(t) = −3 (b) g(t) = 4t…

A: Laplace transform of the function

Q: 6. Find the Laplace transform of the following functions (a) g(t) = et+2+ sint cost+to(t-2).

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Q: Using convolution property of Laplace Transform, solve for y(t) of the following: 1) y(t) = e-3t*…

A: Given that     yt = e-3t * t e3t                   Let  gt = e-3t  and  ft = t…

Q: 1.a Find the Laplace transform of the function F(t) = e-2t (cosh 3t + sinh 5t)

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Q: Q4. Apply Linearity property of Laplace Transform to find the Laplace Transform of x(t) = 5e-tu(-t)…

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Q: ƒ (t)= 2te'

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Q: Q2/ from definition of Fourier transform, show that rect (t-5) is sinc (w/2)e-/2w

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Q: 2. Find each of the following transforms: (a) L[x² sin ax];

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Q: Determine the Laplace transform of L(sinh 5t * cos t)

A: Explanation of the answer is as follows

Q: f (t) = cos² (πt)

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Q: 5 The inverse Laplace transform of F(s) = 5² - 2s+5 1 f(t) = 5e²¹ sin 2t f(t) = 5e¹ sin 2t 5 f(t) =…

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