Use the Laplace transformation to solve the problem: x >0, t>0 %3D 2

Q: Find the Laplace transform for :  f(t)= e^3t sin 4t

A: Some Laplace transform formulae: L{eatsinbt}=bs-a2+b2 Given function is: f(t)=e3tsin4t To find the…

Q: x(t) = t³ + 5t – 2 %3D

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Q: f(t)= t³ cost

A: 8

Q: Find the Laplace transform of the function f (t) e2t = e2t using direct integration.

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Q: Using the laplace transformation formula, ∫ f(t) e^−st dt evaluate L[3 sin(-3t) – 4 cosh(-4t)]

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Q: Find x(t) and Y(t) using Laplace transform.

A: The given pair of equations dxdt=2x-3ydydt=y-2xx0=8, y0=3

Q: Use Laplace transforms to solve t + f(t) = f sinh(w)f(t-w)dw

A: Given equation is t+f(t)=∫0tsinh(w)f(t-w)dw Take Laplace transform on both sides.…

Q: Find the Laplace transform of f(t) = cos(2t) * u

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Q: PROBLEM B dx ·+ 9x = 12 WHERE : x(0) = 1 dt

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Q: L{t³et – e=3t cos7t}

A: Solution

Q: L(e2t t2)

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Q: 1. f(t) = (2e-4t + sin t)²

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the Laplace Transform F(s) of: f(t)=et (ao+a₁t+...+ant)

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Q: Solve the given by using the Laplace transformation.   L[7t^4 + 4 cosh(2t) + 5e^3t + 2 sin(4t) ]

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Q: f(t) = t³ – 2t + 3

A: The given function is ft=t3-2t+3...(1) Here, we have to find the Laplace transform of ft.

Q: find the Laplace transform of f (t). f(t)=tsin3t

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Q: Solve the laplace transforms given t=0 and e=Dandx=1

A: See the solution in the given fig.

Q: Solve f'(t) + f(t)=3 where f(0)=0 using laplace transformation

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Q: 3.) f(t) = e4*sin (3x

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Q: π od T = ¹. Ans: V a

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Q: find the Laplace transform of f (t). f(t)=t^2 cos2t

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Q: f(t) = e-2t-e-3t %3D t

A: The given function is                                           f(t)=e-2t-e-3tt To find the Laplace…

Q: Use the Laplace transformation to solve the following ODE: y''-y'-12y=2e2t, with y(0)=7, y'(0)=0.…

A: Given: The given ordinary differential equation is y''-y'-12y=2e2t with y(0)=7 ,y'0=0

Q: Find the Laplace transform for 1. f(t)=e*(? +2t +5),

A: As per our guidelines, we are supposed to solve only question.Please repost the remaining question…

Q: Use the Laplace transformation, solve the initial value problem y (t)-5y (t)+7y (t)-3y(t)=20 sint: y…

A: See the solution in the given fig.

Q: Solve the following equation using Laplace Transformation Method: dC + aC = B dt (C0) = C.) where a…

A: Take Laplace to both sides of the equation dCdt+αC=B and apply linearity property  .…

Q: Find the laplace transform for the equation f(x) = 2 e^-2t sin4t

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Q: Find the Laplace transform of f(t) = tu1(t). %3D

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Q: find the inverse laplace trans F(s): 2s-3 / (s2+2s+10)

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Q: Use the Laplace transformation method to solve the IVP " – 4y = e-t+ 28(t – 2), y(0) = –1, y'(0) = 1…

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Q: s+ 8 F(s) %3D s2 + 16s + 68

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Q: Find the Laplace transform. f(t)=cos^2(2t)

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Q: Solve the DE using laplace transformation: x'''(t)-3x''(t)-4x'(t)+12x(t)=12e^(-t); x(0)=4, x'(0)=2,…

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Q: Use the Laplace transform to find the solution x(t)

A: [1] x(0) = 0 , x'(0) = 0 [2] x(0) = 0 , x'(0) = 2

Q: Find the Laplace Transformations of the following functions i. L{(sin t + cost)² - cos² 3t}…

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Q: Find the inverse laplace of (2s-1) F (s) s2 –6s+18

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Q: Solve using the method of Laplace transforms /" – 2y' – 84 = 0 y (0) y (0) %3D 3.

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Q: 0st<3 f(t) = { f(t) = t2 3

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Q: we are asked to solve using laplace transformation, the given is y'''+3y''+3y'+y=30x^2e^x

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Q: Use a Laplace transform to solve y" + 16y = 6 (1 –).y(0) = 1, y'(0) = 0. %3D 4

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Q: Find the Laplace transform of Į 0, = { - 6t + 15, 123 t< 3 f(t) = F(s) =

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Q: f(t) = 5te-²t cos(3t)

A: We have to solve the given problem by Laplace transform.

Q: find the inverse laplace tramsform 3/(s-2)^2+4

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Q: Find the laplace transformation of the following 3x' +34 + 5X = 25 Cost X(0) = 2 ノ 2x` - 33' = 5…

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Q: Find the laplace transform of f (t) = 2t1 – 3et + 10 cos 2t %3D

A: We will use property and tables of laplace transformation

Q: f(t) = e3t f(t) = t3 %3D

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Q: c ] s(at)sinh(af)

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Q: Q2: Solve y" – 4y' + 4y = t?e', y(0) = 1, y'(0) = -1, using Laplace transformation.

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Q: Find the Laplace transforms of the functions: f(t) = t²

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Q: b) f(t) = t*e3t

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