3. (а) 5е () 2е 21 -2t

Q: 4. Find the Laplace transforms of the functions: (a) f(t) = t² (b) f(t) = t – 2e3t

A: a) f(t)=t2b) f(t)=t-2e3t

Q: Find the Laplace transform of the following 2. 2y+3y" - 23y' - 12y = 5t-7, y(0) = 0, y'(0) = 0, y"…

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Q: Find the Inverse Laplace Transforms of the following: 5 1. F(s) = s. (s² + 3s + 2) 2. F(s) =7 (67 +…

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Q: 2s-3 L-1 s2-4s+8

A: To solve this question first we simplyfy the given function and then use the inverse Laplace…

Q: 1. Determine the following Laplace transforms: s+% L*(- `s² – 3s + 9' i) ii) L((1² +e cos 2at…

A: As per our guideline we are supposed to answer first three subparts.kindly repost other question.…

Q: 3. Determine the inverse Laplace transforms. 3s2 + 8s + 9 1-J = (1)f (8) (s + 2)3

A: Since you have asked multiple question, we will solve the first question [3 (a)] for you. If you…

Q: Evaluate the inverse Laplace transforms of the following: 2 1 4 1. s+9 S- 5 20 2. E 1 [s+3 5s –3

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Q: Determine the particular solution of y"–3y'+2y=4e"; y(0)=-3,y'(0)=5 using Laplace and Inverse…

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Q: 2. Find the laplace transforms 3. Find the laplace transforms of f(t) = et³ of f(t) = ¹e²t (2t)

A: Note: There is no standard form of Laplace transforms of f(t)=et3. For (3),     L14e2t2t=14·…

Q: 1. (a) 2t – 3 (b) 5t²+41 – 3

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Q: - 3t +2 (b) 24 2. (a) 15

A: Topic = Laplace transform

Q: L(e2t t2)

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Q: If y" -6y' +9y = 5t², y (0) = 0, y' (0) = 1, what is the Laplace transform of y? 8 s²-68+9 + 10…

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Q: Find the Laplace transforms of the given functions. 3. h(t) = 3sinh(2t) + 3sin(2t)

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Q: Determine the Laplace transforms of 3, 0 12

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Q: Solve the laplace transforms given t=0 and e=Dandx=1

A: See the solution in the given fig.

Q: 2 1. Prove that L(2) S

A: To prove L2=2s

Q: y" + 3y' – 4y = 6e2t=3, y(1.5) = 4, y'(1.5) = 5

A: Solve by Laplace transform

Q: Q3: Find the solution of the Laplace transforms of the following functions: -3s²-12s-87 1) L-1…

A: Given problem:- Find  L-1[(-3s2 -12s-8)/(s+2)3]

Q: 1. Determine the following Laplace transforms: i) Le cosh' at) L'+% -3s+9" ii) 3s +5 iii) -2s+1

A: As per our guideline we are supposed to answer first three subparts.kindly repost other question.…

Q: Determine the Laplace transforms of the following functions. (a) 3e-4t - 5e4t (b) sin 4t + cos 4t…

A: Dear student, According to our guidelines we can answer only three subparts of the questions.

Q: 2. Determine the inverse Laplace transforms of the followings: (a) L-1 s2+2s – 3 4s - 3 (b) L-1 s2…

A: Laplace Transform: The Laplace transform is defined byℒf(t)(s)=∫0∞f(t)e-stdtwhere f(t) is defined…

Q: (b) 5t²+41 – 3

A: To determine the Laplace transform of the function: f(t)=5t2+4t-3 Note that: Ltn=n!sn+1

Q: 5. Using Laplace transforms, solve the IVP 1, 01

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

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Q: Ive the given IVP using Laplace transforms. "-7x'- 8x = 0 x(0) = 1, x'(0) = -3

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

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Q: )- 33 Use the method of Laplace transforms to solve each IVP. 5. y" - 2y' + y = 2t – 3, y(0) = 5,…

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Q: Evaluate the inverse Laplace transforms of the following: 1 4 1. L s+9 s- 5 20 1 7 2. s+3 5s –3 6s –…

A: We have to evaluate the inverse Laplace transform. 1. L-12s-1s+9+4s-5…

Q: Please solve this differential equation question. thanks!

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Q: Find the Laplace transforms of f(t) = e(3t-7) cos3(6t).

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Q: In numbers 3 and 4, evaluate the given Inverse Laplace Transforms. L-1{ 41 41 + + - (s+3)5} s-3…

A: The Inverse Laplace Transforms of the given functions are determined as shown below.

Q: Determine the Laplace transforms of * 3, 0 12

A: We use the definition of Laplace transforms to answer this question. All that is required is to…

Q: 3. Determine the inverse Laplace transforms. (-2s + 5) -5s – 20 (b) f(t) = L ' 1(s² + 4) (s + 1) ]…

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Q: Solve the following IVP by using the Laplace transforms. Choose ONE problem: (Hint: No need to…

A: y''+3y'+2y=2  if 0<t<1y''+3y'+2y=0  if t>1y(0)=0, y'(0)=0 first we need to convert f(t)…

Q: 4. (a) 4 sin 3t (b) 3 cos 2t

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Q: (4) 3 2s-4 1 s2+4s+4 s+2 s2+4s+5 5s-6 s2 –3s

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Q: 15) Use Laplace transforms to solve y" +16y=8(t-2n), y(0) = 0, y'(0) = 0.

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Q: [4s-3 L-1 s2+4]

A: We have to find Inverse Laplace Transform of given function using Following Formulae,

Q: 1 (² 1

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Q: 1. Evaluate the following Laplace transforms: 25 +3 fe (5+3)=6 =} b. 2¹ inverse 5S+1 (S-2)6

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Q: Determine the following Laplace transforms: i) L cosh at) i) -35+9 iii) Ls +5 7-23+1 2s+1 iv) Ls+…

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Q: 3. (а) 5е (b) 2е 21

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Q: Sole the IVP using the method of laplace transforms.   w''-10w'+25w=25t+140   w(-2)=1   w'(-2)=-12

A: According to the given information it is required to solve the initial value problem using laplace…

Q: Find the laplace transform of F(s) = (s ^ 2 + 5s + 19)/((s ^ 2 + 4)(s ^ 2 + 9))

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Q: Please solve this Differential Equation question. Thank you!

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Q: s+1 L-1 (s+3)2+16)

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Q: (4) Find Laplace Transform F(s) for the variable x or y in the equations a-y"+2y'-3y=32e"; y'(0) =…

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