4. Solve the following initial value problems using the Laplace transform: a) y' + 3y = 0, y(0) = 1.5. b) y" - y' - 6y = 0, y(0) = 11, y'(0) = 28 c) y" - 4y + 3y = 6t8, y(0) = 0, y′(0) = 0 d) y" + 3y' +2.25y = 9t³ +64, y(0) = 1, y'(0) = 31.5 e) y" + 3y' - 4y = 6e²t-3, y(1.5) = 4, y′(1.5) = 5

Q: Q1 (a) Using the first shift theorem, find the following Laplace transform: L{e-2tcos3t)

A: The given question can be solved as shown in step2.

Q: L-¹ s+2 2s²+4s+ 7

A:

Q: Find the inverse Laplace transform of the following function by using Theorems and tables 2s + 5 +…

A:

Q: Find the inverse Laplace transform of the following function by using Theorems and tables 2s +5 s* +…

A: Recall the following.…

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A:

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Q: Find the Laplace transform of t²e-⁹t

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Q: Q1/ Find the laplace transform for the following 1 - e-6t.sin(10t-8)

A: By using properties of Laplace transform we solve the given problem as follows :

Q: Find the Laplace transform of L(t5)

A: The Laplace Transform of f(t) is given by, L{f(t)}=   ∫∞ 0   e^-stf(t)dt Here f(t)=t^5 So, L(t^5)= ∫…

Q: Compute the Laplace Transform of f(t) e-St using the definition of the transform. (Just listing the…

A: ANSWER:

Q: Find the Laplace Transform for the function e-Nt sin²(Nt)

A:

Q: Find the Laplace Transform of: e-2 -2t sin2t + e3tt2

A:

Q: f(t) = e-3t sin(4t).

A: Introduction: Laplace transform is named in honour of the great French mathematician, Pierre Simon…

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A: To prove: State and explain the convolution theorem for Laplace transform.

Q: Evaluate the given Laplace transform: L(cos^2 3t)

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Q: Find the Laplace transform of f () = a2. Answer: 3 a. b. C. d.

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Q: WHAT IS THE LAPLACE TRANSFORM OF THIS? -3(1-cosh 377t) t.

A:

Q: 4. Find the inverse Laplace transform of 1/(s² + 4s + 5) Enter your answer

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A:

Q: 3s + 4 Find the inverse Laplace transform, L-1 ((s + 1)2.

A:

Q: Please do the Fourier transform of the following formula u₁(xo, Yo) = exp(- exp(-xo+yo) wo

A: Given: u0x0,y0=exp-x02+y02w02 To find: Solution

Q: What is the Laplace transform of (1 + e4t)?

A:

Q: Determine the Laplace Transform of est cos 5t .

A:

Q: Problem 3. Which gives the inverse transforms of the given s-domain function?…

A: Given problem:-

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A:

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A:

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A: Given: Signal, y=coshtTo find: Fourier transform of the given signal.

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A: Given: Signal, y=sinhtTo find: Fourier transform of the given signal.

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A:

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A:

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A: Here we will use Laplace transform method.

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A: To write t^3 in Python, you can use the `**` operator for exponentiation.

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Q: Q3): Find the Laplace transform of (u²-u+e") du.

A:

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: We will find out the required value.