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Find the Laplace transform of the following functions. (a) f(t) = sin(2t) cos(2t) (h) f(t) : 66‘“ sin(3t) (C) f(t) = 6te’2t sin(3t) (d) fit) I tzeg‘t Find the inverse Laplace transform: a (a) Frs) 1-5-6

/in /by

Find the Laplace transform of the following functions.
(a) f(t) = sin(2t) cos(2t)
(h) f(t) : 66‘“ sin(3t)
(C) f(t) = 6te’2t sin(3t)
(d) fit) I tzeg‘t Find the inverse Laplace transform:
a (a) Frs) 1-5-6
_ 4—
(1)) F05) _ (s+2)(52+9)
_ 5+4-
(0) PIS) _ 52+4s+29
The transform of the solution to a certain differential equation is given by Y(s) : 3:; Determine the solution y(t) of the differential equation. Suppose that the function y(t) satisfies the DE y” 7 2y’ 7 y = 35in(4t), with initial values y(0) = *1,
y’(0) = 1. Find the Laplace transform of y(t). Consider the following IVP: y” + 631′ + 13y = 0, y(0) = 2, y’(0) = —1.
(:1) Find the Laplace transform of the solution y(t).
(13) Find the solution y(t) by inverting the transform. Consider the following NP: y" — 3y’ — 10y = 5, y(0) = 2, y’(0) = —4.
(:1) Find the Laplace transform of the solution y(t).
(in) Find the solution y(t) by inverting the transform.

 
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