1.) Determine the laplace transform of the following functions: y" – 3y' + 4y = 0; y(0) = 1, y'(0) = 5 %3D

Q: y" – 7y' + 12y = 4t where y(0) = 1 and y'(0) = 0

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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: Use the Laplace transform to solve the following initial-value problem for a first-order equation.…

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Q: Solve the equation using Laplace transform y" - 6y' +9y t²e³t, y(0) = 2, y'(0) = 6. =

A: Introduction: There are many different ways that are applied to solve an initial value problem. One…

Q: 7. Evaluate y" + y' = t; y(0) = 1 , y'(0) = -2

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Q: 3. Use Laplace transform to solve the IVP y" + 9y = e', y(0) = 0, y'(0) = 0. %3D %3D

A: Laplace transferom, solve the intial value problem

Q: 3). y" + 2y' - 8y = 24, Given the IVP: y(0) = 0, y'(0) = -6. A) Use the Laplace transform to find…

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Q: Find the Laplace transform of: y" + 5y- y = et - 1; y(0) = 1, y'(0) = 1

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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: 3t y" - y' - 6y = t²e³t - 4t², y(0) = 0, y' (0) = -1

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Q: y" + y' = t; y(0) = 1 , y'(0) = -2

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Q: Find the formula for the Laplace transform of the derivative of a function y'. Use the initial…

A: The solution is given as follows

Q: . Find the laplace transform of the 1VP: y" - 4y = et + t, y = y'(0) = y" (0) = 0

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: Find the Laplace Transform of (i) e3(2cos 5t - 3sin 5t) (ii) e2tcos² t 4t (iii) e**sin 2t cos t

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Q: Solve the IVP using Laplace Transform y" = y + 2y, y(0) = -2, y (0) = 3.

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Q: y""-4y" +5y'-2y = 7t-5, y(0) = 0, y'(0) = 0, y"(0) = -2

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Q: Please help me find the laplace transform of the following equation: 0.00174y''+0.295y'+25y=200u(t)…

A: If Ys is Laplace transform of yt. Then Laplace transform of y' and y'' when y(0)=0, y'(0)=0 is sYs…

Q: Find the Laplace transform of the following: 2y+3y"-23y - 12y = 5t-7, y(0) = 0, y'(0) = 0, y" (0) =…

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Q: C. Time Differentiation. Determine the Laplace Transform of y(t) given all the initial conditions…

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Q: C. Time Differentiation. Determine the Laplace Transform of y(t) given all the initial conditions…

A: We have to solve the given problem by Laplace transform technique.

Q: ii. f(t)= e*tsinhrt 't sinh at

A: Laplace transform formulae: 1. Ltnf(t)=(-1)ndndsnLf(t) 2. Leatf(t)=Lf(t)s→s-a Given: f(t)=e3ttsinhπt

Q: Determine the Laplace transform of the function. a) [4+sin(31)+5e²]- b) Z[6r'+2t’e" +sinh(4)].

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Q: 7. F(t) = cos?- sin? 2 8. F(t) = cos ( bt 9. F(t) = 8 sin- cos %3D

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Q: Using Laplace transform, sole cỳ"+y= cos x, where y (0) = 0 = y'(0)

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Q: у" + 2y'— Зу%3D бе 3t У (0) — 0, у' (0) - 0 %3D

A: Here we use simple Laplace transform to solve this