y' = 8x x(0) = 1 %3D x' = 2y y(0) = 0 %3D

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

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Q: Q1\ Find the Laplace transform for the following function: f(t) = - 24 t5/2 + t e3t sin (6t)

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

A: Recall the following.…

Q: Find the laplace transform for the expression : e (f +3t + sin(5t))

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Q: find the laplace transform of the equation: f(t)= 2t^3 e^-4t

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Q: 4. Find L'{ -}. Give table number. 3-5S

A: We have to find L-123-5swe are going to use the formulaL-11s-a=eat ——(*)

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: f (t)%3 3e ' cosh ( In 2r)

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Q: 2s + 16 s² + 4s + 13

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Q: Let f(t) = e^t if 0=1   Write f(t) using step function and find the laplace transform. Also,…

A: We have to write f(t) using step function and find the laplace transform. Also, draw the graph.

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

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

Q: sin 2t (i) Find the Laplace transform of

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Q: xct) = 3(t/4) e

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Q: an initial investment of 1500 thousand dol ollars at the end of each of the next two qua The…

A: Given: Initial Investment=$1500000 Further investment=$250000 (Quarterly) Operating cost=$120000…

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: Q3\Find the Laplace transform of: a) t et * sin(4 t)

A: Given  f(t)= tet sin4t

Q: Find a general solution of the following ODE using Frobenius method. x(x-1)y" + (3x-1)y' + y = 0

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Q: 2. Verify the following property of the Fourier transform: F(u(x + a)) = e-ial a(z)

A: Given::- Verify the following property of the Fourier transform: F(u(x + a)) =e^ -ia xi hat u( xi).

Q: 3 s + 10 s – 40 (t) (s³ – 4 s² – 7 s + 10) (s – 4) s

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Q: Q3\ Find the Laplace Transform to the following function L sin2t cos3t

A: Using Laplace transform

Q: Find the inverse laplace transform of H(s)= 8/(3(s^2) + 12) + 7/s^5

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Q: Determine the Laplace transform of L(sinh 5t * cos t)

A: Explanation of the answer is as follows

Q: 4. Find the Inverse Fourier transform of Te-l@l.

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Q: Determine the Laplace transform of the functions shown and simplify . 23t^2 - 4e^2t

A: Some Laplace formulas: L(t2)=2s3 Leat=1s-a

Q: Find the Laplace transforms of the functions. f(t) = Cos^2(2t)

A: Let ft=cos22tTo find: Laplace transform of the function ft.

Q: Find the inverse Laplace transform. F(s) = 1/s - 2/s^5/2

A: This question related to inverse laplace transform.

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

A: Solution:-

Q: Apply the definition of the Laplace transform to find sin bt.

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Q: Find the Laplace Transform 3 1- f(t) = 3t4 – 2 ti+ 6

A: