Solve the initial value problem below using the method of Laplace transforms. w" - 6w' + 9w = 9t + 30, w( - 2) = - 1, w'(- 2) = – 4 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. w(t) =| (Type an exact answer in terms of e.)

Q: Find the Laplace transforms of the following functions: 3 -4 (s + 3)² + 16 4s2 – 4s + 2 (s – 1)3 13…

A: Since you have posted multiparts questions and we can answer 3 subparts. So answered 1, 2 and 3.

Q: 2. Finish solving each IVP by finding y(t), the inverse transform of Y(s). Do not use convolution…

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Q: Determine ¹{F}. s²F(s)-sF(s)-30F(s) = 2s²2² +8 2 S + 4s

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Q: Determine £¹{F}. F(s) = 3s² +32s + 77 (s-3) (s² +2s+10) Click here to view the table of Laplace…

A: Here given that F(s)=3s2+32s+77(s-3)(s2+2s+10) We have to find the inverse Laplace transform of F(s)…

Q: Determine £¹{F}. SF(s) - 2F(s) = 4s + 5 s² +45 +4 Click here to view the table of Laplace…

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Q: Determine L '{F}. s?F(s) s+5 + 3sF(s) – 10F(s) = %3D 2 s+ 6s

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Q: Determine {F}. F(s) = 7s³ - 15s² - 9s +27 3 3 s³ S (s - 3)

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Q: The inverse Laplace transform of -3s² - 12s + 133 (s+2) (s² - 6s+13) is: + qeßt cos(wt) + reßt…

A: The inverse Laplace transform of  is:, where are constants with .

Q: Determine the inverse Laplace transform of the function below. 2s - 54 5s² - 70s+325

A: The given Laplace function is .To find the inverse Laplace transform of the function.

Q: Determine £¹{F}. F(s) = 3s² + 42s + 119 (s + 5)² (s + 1) Click here to view the table of Laplace…

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Q: Determine ¹{F}. F(s) = 4s² +47s+129 (s+ 5)² (s+3)

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Q: Determine L {F}. 1 F(s) = 8s² +52s +78 (s - 3)(s² +4s+13)

A: Given:

Q: Laplace transform a. L- (¹) 48 b. L-¹ { 1/2-) S5 C. 1 L-1 (2435) s²+3s. :-1 (432 +1} d. L-1

A: We have used standard formulae of Laplace transform.

Q: Determine ¹{F}. F(s) = 7s² - 14s +3 s(s-6)(s-7) Click here to view the table of Laplace transforms.…

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Q: 3 Triangle ABC is to be reflected over the x-axis to form triangle A'B'C'. 21 B -6-5 -4 -3 4 5 -1 -3…

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Q: 25. Find the general solution of the equation dy = 2y + 2e-. dt (This equation is linear, but please…

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Q: Q1\Find inverse Z transform for the following:- Z-1 2-3z¹+z-² -1 x(z) =

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Q: * + 5x + 6x = 5sin (2t)

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Q: 1 L 's2-8s+25-

A: Find L-11s2-8s+25 as follows First rewrite the expression 1s2-8s+25 as shown below.…

Q: Determine £¹{F}. 2 4s s²F(s) + SF (s)-12F(s) = - 2 +7 s + 6s

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Q: Let û(q) and (a) be the Fourier transforms of u(x) and (x) respectively. What is the Fourier…

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Q: Find the Inverse Laplace transforms of the following functions:   (4s + 2)/(s2 +6s + 34) 1/…

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Q: 15. Solve the IVP using Laplace transforms. x'(t) = t?, x(0) = 4

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Q: Q3/ find the inverse Z transform for the following 8z (2z-1)(4z - 1)

A: In this question the denominator is    (2z-1)(4z-1) =8z2 - 6z + 1   So the question can be done as…

Q: Determine ¹{F}. F(s) = 3 10s³ - 30s² - s +6 3 s³ (s-6)

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Q: How did they get Y(s)? I tried, but I don't get how to convert the y' notation.

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Q: Determine £¹{F}. F(s) = 2 6s - 11s+5 s(s-6)(s-5) Click here to view the table of Laplace transforms.…

A: Given Fs=6s2-11s+5ss-6s-5   To Find: ℒ-1F

Q: Determine £¹{F}. 25² 2s +67s+218 F(s) = 2 (S-2) (s² £¹{F} = +8s +25) Click here to view the table of…

A: We find required Inverse Laplace Transform.

Q: Find the inverse Laplace transform of L- s-37+4J- 3 (++3)²+4 3 3t e e 3t sin2t sin2t (s+3)2 (C) L"f…

A: Answer

Q: Determine the inverse Laplace transform of the function below. 11 (2s+3)4 Click here to view the…

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Q: Determine the inverse transforms of the following. 2s 6 (a) (c) (S-2) (S-4) (b) 5s-8 s(s - 4) $²25…

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Q: 50, dex(+) = -25 (+ + 2) + 25 (1-0) + 15 (t-1) at 2 = -√(x + 2) + 251f) + 5lt-2) By using…

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Q: Determine £1 '{F}. 4s +5 sF(s)-2F(s) = s²² + 4s +4 Click here to view the table of Laplace…

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Q: Determine L '(F). -s+50s +311 F(s) = (s- 1)(s+ 10s + 61) Click here to view the table of Laplace…

A: Inverse Laplace transform of a function F(s) is the piecewise-continuous and…