Transform the differential equation 9y" +14-81 - 126y= 5et y(0) = 0 3/(0) = 0 3'(0) = 1 into an algebraic equation by taking the Laplace transform of each side. Use Y for the Laplace transform of y, (not Y(s)). 0-0 Therefore Y - 8+1 Taking the inverse Laplace transform we get

Q: The signal x() exp(-at)u(t) is passed as the input to a system with impulse response…

A: We have given a signal ..with the help of the Fourier transform we find energy ..the procedure is…

Q: Describe in your own words the method you would use to find the Laplace transform of the first…

A: The Laplace transform of function f(t) is given by Lft=∫0∞e-stft dt and is denoted by F(s). We can…

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…

Q: Find the solution of the differential equation which satisfies the indicated conditions: 1. y" – 3y'…

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Q: Compute the Laplace transform. Your answer should be a function of the variables: L2+ u₂(t)e-³¹…

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Q: Use matrix to solve for X(s) and Y(s) in the equations below and find the laplace transform of X(s)…

A: To solve the given problem Simplify for X(s) and Y(s)  Using inverse laplace transformation solve…

Q: Solve System of Linear differential equations using Laplace transform: Provide all steps First order…

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Q: Find Y(s) is the Laplace transform of Ay" + By' + Cy = e2 given that y(0) = y'(0) = 0 %3D a. Y(s) =…

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Q: into an algebraic equation by taking the Laplace transform of each side. Use Y for the Laplace…

A: Given                   with              Take Laplace transform on both sides then…

Q: 1. (a) Use the Laplace transform method to solve the IVP: y"+4y=4-4u(t-л): y(0)=0, y'(0) = 0 (b)…

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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: y′′ − y′ − 6y = 0 y(0) = 11 y′(0) = 28 find laplace transform explain all steps

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Q: Using Laplace transform solve the following shifted data IVP y' – 6y = 3(t + 5) y(-5) = -6

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Q: x^2y′′ + (3/2xy′ + [(1/36)x^2/3 − 7/144]y = 0 z = (1/2)x^1/3, w = yx^1/4 Solve it using the…

A: The transform method can be used to find the solution to the differential equation x^2y′′ + (3/2xy′…

Q: Apply the translation theorem to find the inverse Laplace transform of the following function. 5…

A: Here we have to find out f(t) using inverse Laplace transform.

Q: Determine the Inverse Laplace Transform of the functions using the Laplace of Integrals and…

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Q: Laplace transform of x(t) = cos(4f)u(t) %3D 16 X (s) = s* +16 4 X (s) = s* +16 X(s)D s? +4 X(s) = s´…

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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: 7y" +46y" 175y' - 1150y = 4e t y(0) = 0 y (0) 0 y" (0) = 1 into an algebraic equation by taking the…

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Q: dt? + w?) G(t) = 6(t) () 1. Now using the Fourier transformation on both sides of equation 1 and…

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Q: Find the Inverse Laplace transforms of the following functions:   (4s + 2)/(s2 +6s + 34) 1/…

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Q: 5s-1 JA function has a Laplace transform of F(s) : If this function is %3D s²-1 multiplied by e',…

A: The given Laplace transform is Fs=5s-1s2-1, if this function is multiplied by et. Calculate the new…

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: Q4.) F(s) L' = 45+93 252+85+40 } 45+9 252 = = 2 = +85+40 =2 2 L" { -1 L+ تو 2/2-1 -2t ? (pat し S+…

A: Here we use the sum and product by scale of Laplace transformation.

Q: If F(w) is the Fourier transform of f(t), then the Fourier transform of g(t) = -e3it f(t) may be…

A: Here, gt=-e3jtft

Q: How to solve the Laplace transform of the following equation: W(t)=cos(3t) - cos(7t) Please write…

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Q: What is the Fourier transform of: f(t)=sgn(t) e? Your answer should be expressed as a function of w…

A: Given a function ft=7i2sgnte−8t Explanation ft=7i2e−8t       for t>0 ; t>0 sgnt=1−7i2e8t…

Q: Use formulas from this course to find the inverse Laplace transform (a) L-1{+1) 2s+1 1 252+8 (b)…

A: Solution:

Q: Find the Fourier transform specified in part (a) and then use it to answer part (b). (a) Find the…

A: In part (a) we have to find the Fourier transformation, Given, f(γ,p,t)=e-γtsin pt  t>0,0…

Q: ısform of cos( @E transform of e

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Q: The following is an IVP: Let's introduce Y(a) = C(v(t)) +4y= cos(2), v(0)=3, (0)-8. Part 1 Apply the…

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Q: Using only the Laplace transform table to obtain the Laplace transform of the following functions:…

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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: The problem is related with Laplace transform.  First in part (A), we have to show that Ltnyt =…

Q: x' + æ = 9+ 5(t – 2), x(0) = 0. Find the Laplace transform of the solution. X(s) = L {x(t)} help…

A: Given that, x'+x=9+δ(t-2),x(0)=0 To find the laplace transform for the given equation, Take,…

Q: 1. Find the laplace transform of 2e^(3t) sin 4 t 2. Simplify i²⁹ + i²¹ + i 3. Write in the form a…

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