· y"(t)+5y'(t)+4y(t) = 0, y(0) = 1, y'(0) = 0

Q: Suppose solving an equation by Laplace transform results in Y(s) = s2 + 64' Evaluate y(7).

A: We have to solve given problem:

Q: Prove that for a constant function f(t)= C, the Laplace transform can be given as. F(s)= Z C= S

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Q: Determine, with justification, whether the series converges absolutely, converges conditionally, or…

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Q: 6. Find the inverse Laplace transform of the function (3²-²)(as + b) I(s) = (s² + a²) (s² + 3²)

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Q: Find the Laplace transform of f(t) = te-5t.

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Q: 17 Find the inverse Laplace transform of F(s) 82 + 100 f(t) = %3D

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Q: (Exercise 23 on page 225) Find the inverse Laplace transform of the function using the Heaviside…

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Q: Calculate the Laplace transform of the expression f(t) = sin tu(t – 2n) -

A: Given function: We have to calculate the Laplace transform of the given function.

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: Write the differential equation and then determine whether you have overdamped,critically damped,or…

A: Introduction: The differential equation of motion of an unforced damped harmonic oscillation is…

Q: 7. Use the Laplace transform to solve the difference equation 3x (t) 4x(t-1) = 1, x(t)=0 for t < 0.…

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Q: Ose the definition to find the Laplace Transform of the given function [t, 0St<1 f(t)=} |1, t21

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Q: Find the inverse Laplace transform of F'(s) f(t) = = 6s - 16 s²4s +3

A: The given problem is to find the inverse Laplace transform of the given function F(s). Given F(s)…

Q: Use (8), • S* f(1) dt = £^¹{F(5)}, to evaluate the given inverse transform. (Write your answer as a…

A: we know that laplace transform of e^(at) is (1/(s-a)).