Given that cosh at = 1/ ) and sinh ất = e-at), where a is a constant. By applying the linearity, find the Laplace transform of the following factions. f(t) = cosh at f(t) = sinh at %3D

Q: Find the Laplace Transform of the following: 2. g(t) = t(VF+ 1)?

A: We have to solve given problem:

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: Find the Laplace transform of: (a) cosh at (b) sinh at

A: Given (a)cosh at  and (b)sinh at We have to find the Laplace transform of them…

Q: Q2 \ Determine the Laplace transforms of the following function: t | e-4tt sin? 3t dt L

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Q: Find the cosine transform fe(w) of f(x) for f (x) = -6 if 0 2. f.(w) %3D

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Q: 5. Given that L{ sin VE} = 1/2s T /se-/4. determine the Laplace transform of (1/Vecos vt. %3D

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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 Laplace transform to solve the DE. d²y_3dy = 9 dx² dx where x=0, x=0 and dy=0 dx

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Q: t も c6 10. XCt)> { -8 + -8 t ct-6)? » t >6

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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: 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.Solve the following polynomial equations.  a)  2X3+1=x2+2X

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

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Q: If tan2(2y) – S cost dt = 4 - x² %3D dx

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Q: Determine the Laplace transform of the function tcost using the 2nd derivative theorem.

A: Laplace Transform: Given a function ft defined for all real t≥0, the Laplace transform of ft is a…

Q: f (t) = cos² (πt)

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Q: ii. f(t)= e*tsinhrt 't sinh at

A: Laplace transform formulae: 1. Ltnf(t)=(-1)ndndsnLf(t) 2. Leatf(t)=Lf(t)s→s-a Given: f(t)=e3ttsinhπt

Q: Find the convolution f*g of the given functions. After integrating,find the laplace transform of…

A: Given functions are                                                 f(t)=cos2tg(t)=et now…

Q: Q7. Find the Laplace transform of the periodic function f(t)= sin at for 0<t<¹ 0 for T @ -<t< @ 2π @

A: Sol:-

Q: Find the laplace transform of f(t) =1/4 e^2t sin(2t)

A: Find the laplace transform of f(t) =1/4 e^2t sin(2t)

Q: Use the Laplace transform to solve y' - v = te'sint, y(0) = 0

A: To solve the given IVP, first we take the Laplace transform of differential equation and then we use…

Q: Y(s) = %3D

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