f (t) = e'-²H (t – 3)

Q: 1. Find the laplace transform of sin(t)sin(2t) sin(3t), using est f(t)dt. F 1-4 3 1 r are. ².2.

A: As per our company guideline we are supposed to answer only one qs kindly post remaining qs in next…

Q: Suppose solving an equation by Laplace transform results in Y(s) = s2 + 64' Evaluate y(7).

A: We have to solve given problem:

Q: What is the initial value of f(t) if its Laplace transform is

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Q: 2b. Determine the solution of the following problem using the concept of derivative and integral…

A: The given problem is to find the Laplace transform of the given integral term function.

Q: What is the Laplace transform of y’’ – 6y’ + 15y = 2 sin (3t), with y(0) = -1 and y’(0) = 4

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Q: Find the inverse laplace transform of the problem L-[- u+1 (u+1)²+1! L[f(u}] = F(t)

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Q: Solve the following dynamics equation using the Laplace transform with the initial conditions x(0) =…

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Q: 4. Find the Laplace transform of the periodic function f(t) = |cos(t)|

A: Solution: The given function is ft=cost We know that cosπ+t=-cost Therefore, fπ+t=cosπ+t fπ+t=-cost…

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

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Q: 1. A) Evaluate the integral fe"(1+t sinf)dt by using Laplace transform definition and properties of…

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Q: 1 -s F(s) = e = -+ s2 e-3s

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Q: Use laplace transform to solve the initial value problem; a) y'+y=alpha(t-1),y(0)=2

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Q: 15 Solve the IVP using Laplace transforms. x'(t) = t, x(0) - 4

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Q: use the laplace transform to solve the initial value problem y"+2y'+2y=cos(2t) with y(0)=0 and…

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Q: Consider the following initial value problem, in which an input of large amplitude and short…

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Q: 7. A damping system with a negligibly small spring constant is modelled by x' +bx' = a e1 with…

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Q: dx 4x = 2e2t + e4 dt

A: NOTE: Refresh your page if you can't see any equations. .

Q: For given function f(t) = 2sin(3t) – 3 cosh(2f)+e6t +5 Laplace transform of L(f(t)) and L(1¶ O), dt…

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Q: 4. Use Laplace transform to solve the fowowing Initial -value problem : y" *y =hlt),ylo)=1,y'l=2…

A: In the question it is asked to calculate the initial-value problem using Laplace transform.

Q: Laplace transform of f(t)=te^(at)

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Q: What is the value A 4B for Y(a)= which is Laplace transform of the solution of initial value 16…

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Q: The Laplace transform L{e^-t^2} exists (because it is exponential order), but without finding it…

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Q: 4. If f(x): = cos Tx then the Laplace transform L{f(x)} fthe differential couation(v -x)dx + 2ydy =…

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Q: a. Use the Laplace transform to solve the initial value problem y" +2y'+2y cos(2t) with y(0) = 0 and…

A: The solution is given as

Q: use the Laplace transform to solve the given initial-value problem. dy di -Y= 1 P. | У(0)-0

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Q: 10) Use the Laplace transform to solve the given initial-value problem. y'-y = 2 cos (3t) when y(0)…

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Q: Suppose solving an equation by Laplace transform results in 6 s Y(s) = s² + 64° Evaluate y(").

A: y(s)=ℒ(6ss2+64) =-3(2si(8s)-π)sin(8s)-6cos(8s)ci(8s) y(π)=-3(2si(8π)-π)-6cos(8π)si(8π)

Q: find the Laplace transform of VE cos(3Vf). E{VE cos(3V)} =0.

A: We are given that,  Lcos3tπt=e2.25ss..................................................(1) We are…

Q: 04 Obtain the particular solution for: 2y" +2y= 2 sinx y(0)=0, y'(0)=1 (a) By using Laplace…

A: The solution is given below in the next step:

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

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Q: 6. Solve for the Laplace transform of f(t) = t^2 using the long method

A: Given that: f(t)=t2

Q: Solve the following DE using Laplace Transform Method: 1. y' - y = e5x when y(0) = 2

A: Solve the differential equation, using Laplace transferom

Q: Answer with either True or False. 1. If z = 1 – x – -y² then at the point (0, – ÷ -). =- (0.-)- 2.…

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Q: O xt) tLosh at - sinh 34 + ws (ot - )

A: Properties of the Laplace transform  Laf(t)+bg(t)=aL[f(t)]+bL[g(t)] Ltf(t)=-F(s), where…

Q: 3. e-9t cos(3t) + 5e-2t sin(3t)

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Q: (b) Using Eq. (15.1) to obtain Laplace transform of f(t), = | 5 cos(t)6(t – 2)e¬#dt 5 cos(t)8(t –…

A: Solution

Q: f(t)=e'(4 e2" + 5)?.

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Q: Solve the initial value problem using Laplace Transform of: y'' - 3y'+10y = e-2t when y(0)=0,…

A: Given initial value problem is y''-3y'+10y=e-2t,y0=0, y'0=1 To find the solution of the equation.

Q: If f (t) = ) = CoS ( 4t what is 6 the laplace transform of f (t) ?

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Q: Solve the initial value problem using a Laplace Transform. y "+ 2y' - 3y = sin (2x) ;      y (0) =…

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Q: 8. Use the method of Laplace transform to solve the initial value problem y" – 20y' + a'y = (a –…

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Q: (i) Find the Laplace transform of e" sin 21 dt (ii) Form the PDE by eliminating arbitrary constants…

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Q: Solve the problem: y" - 6y' +8y=sin t, y(0)=y'(0) = 0 a) without using Laplace transform: b)…

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Q: Find the Laplace transform of U2 (t – t) e" sin(2t)dt 2e-25 s (s²+2s+5) 2e-2s s(s²–2s+5) e-2s…

A: Here we will find out the required Laplace transform.

Q: Use the Laplace transform to solve the given initial-value problem. у" + 2y" - у' - 2у %3 sin(3t),…

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Q: Use the Laplace transform to solve the given initial-value problem. y''-y'=et cos(t),    y(0)=0,…

A: Take Laplace transform on both the sides as follows.

Q: 8. Find the Laplace transform of the given function: h (t) = 3 sin h (2t) + 3 sin (2t)

A: Some important Laplace transform formulas: L(sinhat)=as2-a2L(sin(at))=as2+a2 Given function is:…

Q: 2. Solve for the Laplace transform of f(t) = 5 using the long method

A: A detailed solution is given below

Q: y"+ 4y' = cos(t - 3) + 4t, y(3) = 0, y'(3) = 7

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Q: 4. Use Laplace transform technique to solve, y"+2y'+y=4e given y(0) = 2 and y'(0) = -1

A: We have to find general solution of given differential equation using Laplace transform Method.