Q9. Use Laplace transform to solve the ODE. X-4x +3x =-8cos4t, x(0) =0, x(0) = 0 %3D

Q: (c) Use the Laplace transform to solve the following IVP y -2y -3y = e cos(t) y (0) = y(0) = 0.

A: The objective here is to solve the given differential equation using Laplace transform: Given…

Q: k divided by s2 + k2 is the inverse Laplace transform of,

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Q: Q2: Find the Laplace transform for the following periodic functions 1- 0<t<T f (t) =: л — T <t< 2n

A: We solve this by converting it into Heaviside function.

Q: find the inverse Laplace transform of the given function. 5.F(s)=2s−3s2−4

A: Given function is: Since the Laplace transform of: And

Q: Q1/ Solve the following equation using Laplace Transform, when y(0) =0, and y =2 y-3y+2y3D2t

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Q: 8. Find the inverse Laplace transform of the given function: 8s +7 F(s) = s2 +8s + 20

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Q: 2. Find Inverse Laplace transform for the following functions: s2 + 3 b) F(s) (s + 2)²(2s² – s – 1)

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Q: s3-2s2+5s-9 R(s) s2 (s+3)(s+1) 3s+10 W(s) %D s(s-8)(s-6)²

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Q: Q4) Find Z transform for the functions 3) x(t) = te-at

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Q: find the inverse Laplace transform of the given function. 6.F(s)=8s2−4s+12s(s2+4)

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Q: s3 – 2s – 1 L(5(E) = (--s-12)(s² +3) s* +3

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Q: Using the inverse Laplace Transform, we have 1 2 4t e L-1 I (s – 4)3

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Q: ii) F(s) = (- + 10s + 2.

A: The inverse Laplace transformation is below :

Q: Q2:Find the inverse Laplace transform o using convolution 1 F(s) s2 - 3s

A: Here we will use Laplace transform method.

Q: s+7 F(s) = s2 - 3s – 10

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Q: Find the Inverse Laplace Transform of the following: 10 2. F (s) s2 +4s+4

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Q: Q2(a) Solve the Laplace transform for the given function. t cos(21)

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Q3) Evaluate The Following Inverse Laplace Transform 9s 1) L-1 (s²+k )2. 4k2 2) L-1{ } (s²+k )²

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Q: 4. Use the Laplace transform to solve the IVP a" + 4x' + 4x = 4e24, r(0) = 0, r' (0) = 1.

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Q: Solve the following function by using Laplace Transform you 3y^42y = 4; (0)=1; y'(0)=0

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Q: Suppose solving an equation by Laplace transform results in 6 s Y(s) = s² + 64° Evaluate y(").

A: y(s)=ℒ(6ss2+64) =-3(2si(8s)-π)sin(8s)-6cos(8s)ci(8s) y(π)=-3(2si(8π)-π)-6cos(8π)si(8π)

Q: Q4: Solve the following IVP using Laplace Transform. (i) y"-4y'=e^(3t), y(0)=0, y'(0)=0

A: Take  yt→Ysy't→sYs-y0y''t→s2Ys-sy0-y'0 Now taking the laplace equation for the y''-4y'=e3t.…

Q: y" – 3y' + 2y = e-4t У (0) %3D1 у' (0) %3D5

A: Solution

Q: Q2/Solve the following ODE using Laplace transform y" – 2y' – 3y = e', y(0) = 1, y'(0) = -1

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Q: Q5- Find the Laplace transform, if it exists, of each of the following functions f(t)= {3t²6t+ e-5t}…

A: The given problem is to find the Laplace transform of the given functions.

Q: Find the Inverse Laplace Transform. Y (s) (10s + 8) తాతి s3

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Q: Q6/ Find the Inverse Laplace Transform 4-L-1( s-3 )

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Q: 3. Solve for the inverse Laplace Transform of 6(s + 2) (s + 1)(s + 3)(s + 4) g(t) =

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Q: Find the inverse Laplace Transform for 3s2 – 28 Y (s) (s – 4) (s2 + 4)

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Q: Using the inverse Laplace Transform, we have {3 1 1 -sin (3t – 9) Ư(t – 2). 3 e-2s 1 %3D 9s s2 + 9…

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Q: Q6/ Find the Inverse Laplace Transform 1 2- L-1 (s²+9).

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Q: Find the inverse Laplace transform of the following functions by using partial fractions: s2 – 2s +…

A: The Laplace transform of a piecewise function f(t) is given by the formula: If we represent the…

Q: Given: s (s + 3) / (s^2 + 4)(s^2 + 6s + 10) . Express the inverse transform as an integral.

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Q: Solve for the laplace transform x(t) = 4(t/5) e-t/6

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Q: Solve the inverse Laplace transform: 3s s2+4s+13

A: We need to find L-1{3ss2+4s+13}

Q: Q1: Find inverse Laplace transform of the following functions 3s 4) F(s) : s2+2s-8

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Q: Solve for the laplace transform  x(t) = 3(t-5)5

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Q: Q1.Solve the following IVP by mean of the Laplace transform P.D.E. u = a²uxx -∞0 < x < ∞0,0 < t <∞…

A: Disclaimer: Since you have asked multiple question, we will solve the first question for you. If you…

Q: Solve the following ODE using Laplace Transform: 2. у"+2y' - 3у%3Dбе-3t y(0) = 0, y'(0) = 0

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Q: Find the inverse Laplace transform of the given function   F(s)= 8s2   - 4s +12 / s(s2 +4)

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Q: Q2: Find the Laplace transform for the following periodic functions 0<t< T f (t) = A <t < 2n

A: Laplace transform of the periodic function

Q: 06. Solve the nonhomogeneous ODE. y"-6y' + 9y = x²e5x 7. Use Laplace transform to solve the ODE.

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Q1. Using the tables and partial fractions, find the inverse Laplace transform for each of the…

A: The given Laplace Transform is, Fs=12s4+6s-4-8s2+9+s-2s-22+16+5 To find the Inverse Laplace…

Q: Q4. Find the inverse Laplace transform of 2s+19 s²-6s+58

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Q: 11. 3北 x(t) = e to

A: We have to find the Laplace transform of Xt=e3t-1t

Q: 5. Use the Laplace Transform solve the IVP: x' + y = t (4x + y' = 0 x(0) = 1, y(0) = 2

A: Theory : The Laplace transform of a second order linear differential equation : y" +α y' +βy =f(t)…

Q: H.W: Find inverse Laplace transform: 3s+7 1) F(s) = s2-2s-3

A: Given that Fs=3s+7s2-2s-3 To find the Laplace inverse transformation of the above function.

Q: Q9. Use Laplace transform to solve the ODE. x" – 4x' + 3x = -8sin4t, x(0) = 0, x'(0) = o

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Q: Q2:Find the inverse Laplace transform o using convolution F(s) = 1 2 s -3s

A: Convolution Theorem: If L-1P(s)=p(t) and L-1G(s)=g(t)Then,L-1P(s)·G(s)=∫0tp(u)·g(t-u)duWe have been…

Q: Q6. Find the inverse Laplace transform of (5² +3) s(s² +9)

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