1) Find the Laplace transform of
f(t)=−(2u(t−3)+4u(t−5)+u(t−8))
F(s)=
2) Find the Laplace transform of f(t)=−3+u(t−2)⋅(t+6)
F(s)=
3) Find the Laplace transform of f(t)=u(t−6)⋅t^2
F(s)=
(a) Determine the inverse Laplace transform of F(s) =(2s−1)/s^2
−4s + 6
(b) Solve the initial value problem using the method of Laplace
transform. d^2y/dx^2 −7dy/dx + 10y = 0, y(0) = 0, dy/dx(0) =
−3.
(c) Solve the initial value problem:
1/4(d^2y/dx^2)+dy/dx+4y = 0, y(0) = −1/2,dy/dx(0) = −1.
Please give a detailed explanation, not just the answer. Thanks
in advance!
Use the data in the given table to fill in the missing
coefficients. Round your answers to 3 decimal places.
x
y
2
13.524
7.5
19.125
13
23.463
18.5
28.937
24
33.6
29.5
37.779
35
43.065
y=_____x +_______