Question

transform the given initial value problem into an algebraic equation for Y = L{y} in the s-domain. Then find the Laplace transform of the solution of the initial value problem.

y'' + 4y = 3e^(−2t) * sin 2t,

y(0) = 2, y′(0) = −1

Answer #1

transform the given initial value problem into an algebraic
equation for Y=L{y}Y=L{y} in the ss-domain. Then find the Laplace
transform of the solution of the initial value problem.
y′′+2y′−2y=0
y(0)=2, y′(0)=1

transform the given initial value problem into an algebraic
equation for Y=L{y}Y=L{y} in the ss-domain. Then find the Laplace
transform of the solution of the initial value problem.
y′′′+y′′+y′+y=0
y(0)=4 y′(0)=0 ,y′′(0)=−2

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 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)=__________

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)=?

Find the Laplace transform Y(s)=L{y} of the solution of the
given initial value problem.
y′′+9y={t, 0≤t<1 1, 1≤t<∞, y(0)=3, y′(0)=4
Enclose numerators and denominators in parentheses. For example,
(a−b)/(1+n).
Y(s)=

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 ′+ 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) =...

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)=

The initial value problem
y''' - y" + y' - y = 0, y(0) = 1, y'(0) = -1, y''(0) = 3
is given. If the Laplace transform of y(t) is Y(s), first find
Y(s). Then using Y(s) find the solution of the given initial value
problem.

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