1.) Determine the laplace transform of the following functions: a.) y" – 3y' + 4y = 0; y(0) = 1, y'(0) = 5 b.) y" + 4y' + 8y = sinx; y(0) = 1, y'(0) = 0 2.) Solve the following using unit step: 0, x < 4 - 4)², x > 4 (2t + 1, 0 < tx < 2 3t, t>2 a.) g(x) = {(x – | b.) f(t) = {4" 3.) Solve the equation using discontinuous function: y" + 9y = cos(2t) – U47(t)cos(2t)

Q: æ' + x = 2+ 8(t – 1), x(0) = 0. Find the Laplace transform of the solution. X(s) = L {x(t)} = help…

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Q: (b) x' + 2y' + x = 0, x' − y' + y = 0, x(0) = 0, y(0) = 0 -

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Q: Now let's have you try to use these formulae. Find the inverse laplace transform of y'(t),y''(t),…

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Q: (i) Beginning with the homogeneous version of ODE, find the characteristic equation by letting…

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

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Q: Find the cosine transform fe(w) of f(x) for f (x) = -6 if 0 2. f.(w) %3D

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Q: a' +x = 6+ 8(t – 4), x(0) = 0. Find the Laplace transform of the solution. X(s) = L {x(t)} = help…

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Q: 8. Solve using the Laplace Transform: x" + 4x + 3x = 1 + e -2, x(0) = 0, '(0) = 1.

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Q: Use Laplace transforms to find the equation of the current as a function of time i(t) in a series…

A: Given that,L=0.1 HR=45 ΩC=2·10-4 FV=12 Vi(0)=0q(0)=0

Q: b) f(t) = 3 sin(2t) + 5e³t so

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Q: Use the Laplace transform method to solve the IVP: 2. (a) y"-2y'+y=te', y(0) = 0, y'(0) = 0

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: [2.] Solve the IVP yu+ 6y'+9y= e-*cos 2x COS2X t. Fed the Laolace transform

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