Use the Laplace transform to solve the given initial-value problem. Use the table of Laplace transforms in Appendix III as needed. y" + 49y = f(t), y(0) = 0, y'(0) = 1, where Scos(7t), 0≤t<π 1, t> π Dac(2-[ y(t) = f(t) = +

Q: 5 5 ロジー 12y+y="/sin(x) (0) = 0,(0) 2

A: We have given DE,Taking Laplace transformation on both sidessubstitute the given initial conditions…

Q: 3y" + 6y + 3y = 9, y(0) = 0, /(0) = 6 %3D

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Q: y" + 3y" + 3y = y y (0) = 7, y' (0) = -7, y" (0) = 11

A: We will use following Laplace transformation…

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: 8. y" +9y = 20e y(0); y' ||

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Q: A function f(t) is given as f(t) = e' cos 2t cos t %3! Find the Laplace transform of this function.

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Q: Solve using Laplace transforms. y" - y' + 5y = 58(t- T/6) sin t y(0) = y'(0) = 0 SHOW WORK.

A: To find- Solve the Laplace Transforms. y'' - y' + 5y = 5δt - π6sint         y0 = y'0 = 0     Concept…

Q: Q2 \ Determine the Laplace transforms of the following function: t | e-4tt sin? 3t dt L

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Q: cos x, 0 a

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Q: f(t) = [1 – u2m (t)](2 sin t – sin 2t)

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Q: 6. Solve using Laplace transforms: y' + 3y = e5t, y(0) = 2

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Q: -- solve ÿt y-2y=5é'sint ,y (0)=1 and o)=o using Laplace transforms.

A: We have to find solution by Laplace transform Method.

Q: _aplace transforms

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Q: Use method of Laplace Transforms. y"-6y +13y = 0, y(0) = 1, y (0) = -3.

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Q: cos x, 0a

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Q: 3. State and explain the Convolution Theorem for Laplace transform

A: We have to state and proof  the convolution theorem of laplace transform.

Q: Please fill the blanks (......... is a blank) Solve the IVP (d^2y/dt^2)+49y=?(t-k π) , y(0)=0;…

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Q: f(t) = [1– u2m(t)](2 sin t – sin 2t) U2n

A: Some of the properties of Laplace transformation Lsinat=as2+a2Luc(t)=e-cssLuc(t)g(t)=e-csL[g(t+c)]

Q: f(t) = [1– uzn(t)](2 sin t – sin 2t

A: Solution

Q: If F(s) = {f(t)} and n = 1, 2, 3, . . . , then L{t^f(t)} = (−1)n d^_F(s). dsn Evaluate the given…

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Q: Solve the following ODE 3t. y" – 6y' + 9y = t²et; y(0) = 0, y'(0) = %3D

A: Given The given ODE is y"-6y'+9y=t2e3t. y0=0,    y'0=1 Apply formula…

Q: Use Laplace transforms to solve the IVP y''+1=0, y(0)=1, y'(0)=1

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Q: 3. Find the laplace transforms of f(t) = ¹e²t sin(2t) 2t 4

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Q: 2) Sketch the graph of the following s functions and find the Laplace transfo a) f1(t) = }4 – t, (o,…

A: Given,      (a)    f1(t)=t0≤t&lt;24-t2≤t&lt;40t≥4      (b)    f2(t)=00≤t&lt;1t1≤t&lt;21t≥2

Q: 1. y" − 2y'+5y=0_y(0)=2_y'(0) = 4

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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: Solve the IVP x”+9x = U(t-2)sin[3(t-2)], x(0)=2, x’(0)=0 using Laplace Transforms. Identify xc , xp…

A: The solution is given as

Q: y"+y' = 0; y(0) = 0, y '(0) = 1 cost + sint t + cost + sint A) 1- e-t t-e-t O

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Q: When the Laplace transform is used to solve the IVP: y' +5 y=314, y(0) = 2 1/4+ the following…

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Q: Use Laplace transforms to solve the following initial value problem. x"' + 25x = sin 8t, x(0)=0,…

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Q: Use Theorem 7.4.1. THEOREM 7.4.1 Derivatives of Transforms L{f(t)} and n = 1, 2, 3, . . . , then If…

A: Please find the answer in next step

Q: to solve the IVP with an Use the method of Laplace transforms, impulse right-hand side and simplify…

A: Step 1: Step 2: Step 3: Step 4: