1. Use the Laplace transform to solve the initial value
problem.
?"+4?′+3?=1−?(?−2)−?(?−4)+?(?−6), ?(0)=0, ?′(0)=0
2. Use the Laplace transform to solve the initial value
problem.
?"+4?=?(?), ?(0)=1, ?′(0)=−1
= { 1, ? < 1
where ?(?) = {0, ? > 1.
8)
Use the Laplace transform to solve the given initial-value
problem.
y' − y = 2 cos(4t), y(0) = 0
y(t)=???
9)
Use the Laplace transform to solve the given initial-value
problem.
y'' − 5y' = 8e4t −
4e−t, y(0) = 1, y'(0) = −1
y(t)=?
10)
Use the Laplace transform to solve the given initial-value
problem.
y''' + 2y'' − y' − 2y = sin(4t), y(0) =
0, y'(0) = 0, y''(0) = 1
y(t)=?
Use the Laplace transform to solve the following initial value
problem:
?″+6?′+58?=?(?−4)
?(0)=0,?′(0)=0
(Notation: write u(t-c) for
the Heaviside step function ??(?)uc(t) with step at ?=?t=c.)