1 £{sin?;nt} 2

Q: 1 F(s) V5(s+5.5)5.5

A: The solution is given as

Q: (6) y" +16y = g(t), y(0)=0, y (0)=1, %3D g(t) = { 1, 0<t< T 0, %3D

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Q: 6. 7. 5 (s+3)² 3 s2-32

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Q: If L{f"(t)} = arctan ), f(0) = 2 and f'(0) = 1, find L{f(t)}. %3D

A: Given - If ℒf''t = arctan12 , f0 = 2 and f'0 = 1  To find - ℒft       Formula used - ℒfnt = snFs -…

Q: y" + 4y' + 4y = 2e, y (0) = 2, y (0) = %3D %3D

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Q: 1 s²+4s+4

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Q: sin 3t f(t) t

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Q: 3s+4 -s²+4s+5· a. e2t (3 cost - 2 sint) b.e-2t (3 sint 2 cost) c. e2t (3 sint - 2 cost) d.e-2t (3…

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Q: 0<x <A, x. f(x) = 0, cosine series, period 47 Problem 4: %3D T<x < 2N;

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Q: tind Laplace Transform for The funcfion

A: Laplace transforms are usually used for changing domains of the variable. For example if initially…

Q: 4. Solve the initial value problem: y" + 3y' – 10y = 0, y(0) = 1, y'(0) = 0 -

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Q: S Prove that L(cos 3t) (s²+9)

A: Given L(cos3t)

Q: t 3. Lif(t) = 2t (sin 2t 0 ≤t <2 2 ≤t<π † Σπ

A:

Q: Solve the shifted data IVPs by the Laplace transform. Showthe details.

A: Since the method of Laplace transform can be used only if the initial condition are given at 0. The…

Q: L{12te-³t} 12 a. (s+3) 12 b. (s+3)² 1 C. (s+3)² 12 d.- (s+3)3

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Q: What is the inverse Laplace transform of 1 /[(s-2) ^2 + 9]? C. 3e^ (-2t) D. 2 sin (2t) 5. A. sin…

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Q: Jx + L. f(x) = L, *0 > x> 7- f(x + 2L) = f(x) Problem 2: %3D 0 <x < L;

A: This is the problem of Fourier Analysis.

Q: 0 9. f(t)=t-n 0 if t 2π

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Q: Find the solution of the Initial Value Problem given below by using the Laplace transform method.…

A: Given initial value problem, y'''-5y''+17y'-13y=cos2t,y0=0, y'0=0, y''0=1 To find the solution of…

Q: Solve: L{e-2t + 4e}

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Q: Plz explain this question and provide the steps and details. how does it relate to Laplace…

A: Consider the provided differential equation,

Q: 15. 16. 0.5- 2

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Q: 2s-1 's²-6s+18*

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Q: 2s Prove that L(t sin t) (s²+1)²

A: We can use the concept of Laplace transform in order to solve the given problem.

Q: 51²e-31 – e121 cos 8t 10 (s+3) 3-12 (১-12)-64 10 s-12 ((-122+64 (s+32 10 (s+32 s-12 (-127-64 10 s-12…

A: lets see the formulas we are going to use here L{ tneat } =n!(s-a)n+1               ⋯⋯⋯(i)L{ e-at }…

Q: 2s +3 Deter mine the inverse Laplace transform. of

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Q: o f(6)=} slt-2) t4 8Ct-3) %3D 1]

A: As per bartleby guidelines we only give first question answers.

Q: Solve the shifted data IVP by the Laplace transform. Show the details.

A: We have given a initial value problem, y''-2y'-3y=0 with initial conditions y4=-3, y'4=-17 This is…

Q: f(t)= tuŋ(t)+(4−2t)u₂(t)+(t−4)u(t)

A: