Question

Use the Laplace transform to solve the following initial value problem:

y′′ + 8y ′+ 16y = 0

y(0) = −3 , y′(0) = −3

First, using Y for the Laplace transform of y(t)y, i.e., Y=L{y(t)},
find the equation you get by taking the Laplace transform of the
differential equation

__________________________ = 0

Now solve for Y(s) = ______________________________ and write the
above answer in its partial fraction decomposition, Y(s) = A /
(s+a) + B / ((s+a)^2)

Y(s) = _________________ + ________________________

Now by inverting the transform, find y(t) =
______________________

Answer #1

Use the Laplace transform to solve the following initial value
problem
y”+4y=cos(8t)
y(0)=0, y’(0)=0
First, use Y for the Laplace transform of y(t) find the
equation you get by taking the Laplace transform of the
differential equation and solving for Y:
Y(s)=?
Find the partial fraction decomposition of Y(t) and its
inverse Laplace transform to find the solution of the IVP:
y(t)=?

Consider the following initial value problem: y′′+49y={2t,0≤t≤7
14, t>7 y(0)=0,y′(0)=0 Using Y for the Laplace transform of
y(t), i.e., Y=L{y(t)}, find the equation you get by taking the
Laplace transform of the differential equation and solve for
Y(s)=

Use the Laplace transform to solve the following initial value
problem,
y′′ − 8y′ − 9y = δ(t
− 2),y(0) = 0, y′(0) =
0.
The solution is of the form
?[g(t)] h(t).
(a)
Enter the function g(t) into the answer box
below.
(b)
Enter the function h(t) into the answer box
below.

Find the Laplace transform Y(s)=L{y} of the solution of the
given initial value problem.
A. y′′+16y = {1, 0 ≤ t < π
= {0, π ≤ t < ∞, y(0)=3, y′(0)=5
B. y′′ + 4y = { t, 0 ≤ t < 1
= {1, 1 ≤ t < ∞, y(0)=3, y′(0)=3

Consider the following initial value problem:
x′′−3x′−40x=sin(2t),x(0)=4,x′(0)=3
Using X for the Laplace transform of x(t), i.e., X=L{x(t)},,
find the equation you get by taking the Laplace transform of the
differential equation and solve for
X(s)=

use the Laplace transform to solve the following initial value
problem y”+8y’+25y=&(t-8) y(0)=0 y’(0)=0 use step (t-c) for
uc(t)

Use the Laplace Transform method to solve the following
differential equation problem: y 00(t) − y(t) = t + sin(t), y(0) =
0, y0 (0) = 1
Please show partial fraction steps to calculate
coeffiecients.

Use Laplace transform to solve the following initial value
problem: y '' − 2y '+ 2y = e −t , y(0) = 0 and y ' (0) =
1
differential eq

Use the Laplace transform to solve the given initial value
problem.
y′′−8y′−105y=0; y(0)=8, y′(0)= 76
Enclose arguments of functions in parentheses. For example,
sin(2x).

Consider the initial value problem
y′′+4y=16t,y(0)=8,y′(0)=6.y″+4y=16t,y(0)=8,y′(0)=6.
Take the Laplace transform of both sides of the given
differential equation to create the corresponding algebraic
equation. Denote the Laplace transform of y(t) by Y(s). Do not move
any terms from one side of the equation to the other (until you get
to part (b) below).
Solve your equation for Y(s)
Y(s)=L{y(t)}=__________
Take the inverse Laplace transform of both sides of the
previous equation to solve for y(t)y(t).
y(t)=__________

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