2: Solve the following initial value problem by using Laplace transform 4y" + n²y = 0,y (0) = 2, y' (0) = 0.

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: (28x if |x|1* Find the Fourier transform of (x) = { %3D

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Q: 3. (LT-1) Use the Laplace transform to find the solution to the following initial value problem: y"…

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Q: Consider the IVP y''-y'=-30e3tcos(t), with y(0)=1, y'(0)=-12. Take the Laplace transform of both…

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Q: h(t)=t^2sin(3t) laplace transform

A: Given function is,                h(t) = t2 sin3t (.)  Some properties of Laplace transform :- (i)…

Q: using Laplace transform. S=10h 'T=coh Ft = ht+by - banjos (8)

A: The given differential equation is:y''-4y'+4y=4cos2t;  y0=2,  y'0=5. We have to solve using Laplace…

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

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Q: Use convolution and Laplace transform to evaluate y''+y=sin(t) , y(0)=1 , y'(0)=-1

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Q: 6) Use a Laplace Transform to solve. y(4) - 4y(3) + 6y" -4y' + y = 0; y(0) = 0, y'(0) = 1, y"(0) =…

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Q: 4. (20 points) Use the Laplace Transform to solve the IVP y' +2y 2e", y(0) = 3

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Q: Use Laplace transform method to solve the following initial value problem y′′+2y′+y =3te^−t; y(0)=4…

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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: 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: 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: Solve the IVP y""+y'=e*, y(0) = y'(0) = y" (0) = 0 using Laplace transform.

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Q: (3) A signal has Fourier transform as, 1 sinc (2w X(w) sinc + 2. Compute x(t)

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Q: Using Laplace Transform, solve the following initial value problem Зу' - 4y — sin 2t У) --

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Q: ty"+(4t-2) y'+(13t-4) y=0; y(0) =0; y'(0) =0

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Q: Suppose solving an equation by Laplace transform results in 9 s Y(s) = s2 + 49' Evaluate y(0).

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Q: Use the Laplace transform to solve the initial value problem ty''+(4t-2)y'+(13t-4)y=0,y(0)=0,y'(0)=0

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Q: Solve the shifted data initial value problem by the Laplace transform. Show the details. у" — 2y—…

A: Given differential equation,y''-2y'-3y=0,y4= -3,y'(4) = -17