x"(t) + 4x" (t) + 9x'(t) + 10x(t) = -24te'; when t = 0, x = 0, x' = -4, x" = 10

Q: 8s – 18 Find the inverse Laplace transformf(t) = L¯' {F(s)} of the function F(s) : s2 – 4s + 20

A: Consider the provided the question,

Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y"…

A: Given DE is  y"+9y=5t3 ..... (1) y(0)=y'(0)=0 ..... (2)

Q: y" + y = √2 sen √2t, y(0) = 10, y'(0) = 0

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Q: Find the inverse Laplace transform of the following transfer function: Y (s) U(s) (s+7)2 + 25 50…

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

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Q: Consider the function f(t)t(t-1)u(t-1) - (t− 2)u(t-2) + (t− 3)u(t - 3). 11.1 Write f(t) as a…

A: As per the question, we are given a function f(t) defined in terms of the unit step function u(t).…

Q: (cos(t - 27/3 ) t> 2/3 .Find I f(t) if f(t) = t<0

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Q: 2 Calculate the inverse Laplace of by using Convolution theorem s(s2 +2s+4)

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Q: Solve the Laplace Transform of the given function 6e5t cos(2t) – e7t

A: Solved below

Q: Find the Laplace Transform of the function. Show your work. f(x) = sinh(ax)

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Q: B. L{te²" sin 6t} 21

A: (3) We know that  LtnFt=-1ndndsnfs where LFt=fs and LeatFt=fs-a where LFt=fs

Q: Use the Laplace transform to solve the initial-value problem x" + 4x = f(t), x(0) = 0, x'(0) = 0,…

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Q: f(t) = t2 cos 2t.

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Q: 10. Find the Laplace transform of 10 cos Tt (1 < t < 2)

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Q: Laplace Transform 3.4.8. -4-5y=2+ y(0)=/(0) = 0.

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Q: Apply the properties of Laplace transform including the linearity property, shifting property, and…

A: # we are entitled to solve one question at a time, please resubmit the other if you wish to get it…

Q: Use the Laplace Transform to solve the initial value problem. Show your work. y" – y - 2y = 5 sin x;…

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Q: a) 2-3u(t-5) cost = -t Find the 33 Ordine Lap of

A: The given function is ht=-t cos5t-3ut-5cost To find: the Laplace transform of the given function.

Q: 7. L {f(t)} where f(t) = t sin 2t sin 5t %3D

A: Use the trigonometric identity sin Asin B=12cosA-B-cosA+B to simplify the given function.

Q: L[sin(3t - 4n)]

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Q: #o5 Selve the simultem Eou) equatis m3 using ん·T. プ=1; (()=onx() ナ? -0;1()=y() dt

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Q: S Prove that L(cos 3t) (s²+9)

A: Given L(cos3t)

Q: y" – y = 46(t – 2) + t². y(0) = 0, y'(0) = 2. Con

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Q: 3. Evaluate L{4e-2tt3 +t sint cos t}

A: L4e-2tt3+t sint cost

Q: laplace transform

A: Given function is yt=3e-tcost-2cos2t-sin2t We need to find the Laplace Transform of the function.

Q: 4.0 f(t) = 3 – e-3t + 5 sin 2t

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Q: 8. Solve using Laplace transform: y" + 2y – 3y = 8e¬t + 8 (t – ), y(0) = 3, y' (0) = –5.

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Q: 10. Solve F (1) =1 +2 F (t- u) e 2" du.

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Q: I t los 2t e-を

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Q: Solve the given symbolic initial value problem. у'+ 9y'+ 20y 3D е ""6(t-3); у(0) 3 2, у'(0)%3 - 9…

A: We have to solve the given differential equations using Laplace transform.

Q: dy - 4 - 5y = dy -3t sin(4t) ; y (0) = 3, y (0) = 10 dt2

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Q: L {f{t)} where f(t) = cos nt sin mt, m + n

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: 5. If the Laplace transform of f(t) find F(4s)

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Q: Find the Laplace transform of f(t)=u(t− 3)(2t² +1)+2e³ cos²t

A: The objective is to find the laplace transform of f(t).