23: Find the Laplace transform of following functions (a) ƒ (t) = f²e²¹ cos 5t (b) ƒ (t) = -(1-e') (c) ƒ(t) = ¹e* sin(t) t

Q: y''+y'=0 where y(0)=0, y'(0)=1 laplace transform of derivatives

A: Given that:-  y" + y' = 0 and y(0)= 0, y'(0) =1 We find laplace transform of this differential…

Q: y" – 7y' + 12y = 4t where y(0) = 1 and y'(0) = 0

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Q: Find the firs t derivative of the f anction y=4sin[sselur)] at the Point x= T

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

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Q: Let (t) = Find '(t) '(t)=<

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Q: Find the Laplace transform F(s) of the function f(t) = e"6(t - 3) F(s) = e^(20)

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

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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: Find the Laplace transform F(s) = L {ƒ(t)} of the function f(t) = (9 – t) (u₂(t) — u6(t))

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Q: Use Laplace transform to solve the following IVP y′′(t) = 4y(t) −e^(−t)U(t −1), y(0) = y′(0) = 0.

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Q: Find the derivative of the function. f(t) = V5 + tan t sec²(t) 9 V5 + tan(t)2 f'(t) =

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Q: d Find the derivative e" + sin ax] dx e" – a cos (ax) e" + a sin (ax) e" + a cos (ax) e" + sin (ax)

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Q: What would the inverse Laplace Transform be for the attached function if A = 1+j4 and B = 3+j7?…

A: Step 1: Step 2: Step 3: Step 4:

Q: when 0 k

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Q: b) Find O Using the chain rule to find de x-1 dy of y= dy of y sin 1-xy ) Using the implicit…

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Q: Use differentiation in time domain to solve the the Laplace transform: y"+7y'+12y=21e³t; y(0)=7/2,…

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Q: Use the laplace transform to solve 3r'-y=21;x'+y'-y=0; x(0)=y(0)=0

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Q: 1. Find the equation of a line perpendicular to y = 1 through A(-1, 1).

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Q: Part A how that L(tnf(t)) = (−1)n ((dnF(s))/(dsn)), where F(s) is the laplace transform of y(t). In…

A: Hi, It is multiple sub-parts, I am going to solve the first part only.

Q: d the Laplace transform F(s) of f(t) = 5tu(t – 4) F(s) = (5/s^2+10/s)e^(-5s)

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Q: y"+y' = 0; y(0) = 0, y '(0) = 1 cost + sint t + cost + sint A) 1- e-t t-e-t O

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Q: Find the derivative of: - R(t) = (sin² (3t+1), ln(t² − 1), ²) +1

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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…