Consider the following initial value problem. y" + 10y' + 29y = 8(t = n) + 8(t - 7π), y(0) = 1, y'(0) = 0 Find the Laplace transform of the differential equation. (Write your answer as a function of s.) -7AS TTS e + e + s +1 L{y} = (s²+10s +29) Use the Laplace transform to solve the given initial-value problem. t- ) + ( [ y(t) = 1) · (² – π7) + ( [

Q: Solve the differential equation using Laplace Transform. (b) y" – y" + 4y' – 4y = 10e-t, y(0) = 5,…

A: We will find out the required solution.

Q: y" +6y' + 4y = 10e ; y(0) = 0, y'(0) = -2 Answer: y = et -e-t +e-* 3

A: We are given the differential equation : y''+6y'+4y=10et Taking Laplace transform both sides, we…

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A: In your answer this will be 696 place of 632

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Q: 2y" – 2y' + 2y = -cos(3t), y(0) = 0, y'(0) = 1 6.

A: Given differential equation is 2y''-2y'+2y=-cos(3t)                  (1) y(0)=0, y'(0)=1 Let the…

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Q: the fractal differential equation Day + =1/12 and y(0) = 1, Using Laplace transfo

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Q: xy" – 2(x + 1)y' + (x + 2)y = 0.

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Q: Consider the following initial value problem: x" - 5x²14x = sin(8t), x(0) = 2, x' (0) = -1. Using X…

A: We will use Laplace transformation table  f't  = s Fs− f0f'' t= s2 Fs − s f0 − f0Lsinat=aa2+s2

Q: Consider the differential equation 2y" + ty' - 2y = 18, y(0) = y'(0) = 0. In some instances, the…

A: Given differential equation is 2y''+ty'-2y=18 Also given y0=y'0=0   To Solve: The first-order DE for…

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Q: A: Use Laplace Transform to solve the differential equation with following condition y(0) = 0, y' +…

A: Find the Laplace Transform of given differential equation.

Q: Consider the following initial value problem. у" + 8y' + 25y %3D 8(t — п) + 8(t - 7л), у(0) 3D 1,…

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Q: Use Laplace Transformation to solve the differential equation y-2Ky +Ky=2e*(K+cosKx) (0) =1 and…

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Q: Activity 1: The motion equation of damped mass-spring system as shown in Fig. 1 below is given as…

A: As per our guideline we can solve only first three subparts.Please repost for another question.…

Q: Consider the initial value problem I' + 3r = 45t, r(0) = 2. a. Take the Laplace transform of both…

A: Given differential equation is x' +3x =45 t,   x0=2

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Q: How do I solve for the third order y''' - 4y''-11y' + 30y = 4e^8t + t^2 using the method of 1.…

A: repost the question for other method separately

Q: 2- Solve the fractal differential equation Day + y = 5e²x With a = a = and and y(0) = 1, Using…

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Q: Consider the following initial value problem: x(0) = 2, x' (0) = -1. Using X for the Laplace…

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Q: using Laplace transform, solve the equation below. y'' -2y' + 2y = cos (t)         y(0) = 1,  y'(0)…

A: To find the solution of differential equation we use the properties of Laplace transform of…

Q: Determine the direction and magnitude of the phase shift in f(x) = 3sin(x + n/6) - 2 O n/6 O None of…

A: We have to find out

Q: . Determine the Laplace transform of the differential equation 3y" – y' = et5 - 9y" + 4y

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Q: ve the differential equation using Laplace Transform and Inverse Laplace transform y" - 4y' + 4y =…

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Q: Consider the following initial value problem: x" – 2x' – 24x = sin(7t), x(0) = 5, x'(0) = -1. Using…

A: Given differential equation is

Q: Transform the differential equation 9y" +14-81 - 126y= 5et y(0) = 0 3/(0) = 0 3'(0) = 1 into an…

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Q: b) let R be the disk in the xx-plane centered at the point (0.2) and with radius 2. Calculate JJ₁…

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Q: Q5: You have given the following Differential Equation (D.E): (e) + 4 (i(e) + Si(t) = 5u(t) dr i(0)…

A: Given :d2dt2(i(t))+4ddt(i(t))+5i(t)=5u(t)Using Laplace transformation

Q: Solve the following IVP using Laplace transform

A: Given,           y''-4y'+9y=t                          ...(1)and             y(0)=0,   y'(0)=1…