Question

Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y''-9y'+18y=5te^(3t), y(0)=2, y'(0)=-4

Answer #1

we are given differential equation as

we can take Laplace transform both sides

now, we can plug

y(0)=2 and y'(0)=-4

we can solve for Y(s)

now, we can take inverse Laplace transform

**.............Answer**

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.
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)=

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) =...

Use Laplace Transforms to solve the initial value problem for
y(t). Show all steps. Circle your answer.
y''+ 6y' + 9y = 90t^(4)e^(−3t)
y(0)= -2 , y'(0)= 6

Use the Laplace transform to solve the given initial-value
problem. y'' + y = δ(t − 8π), y(0) = 0, y'(0) = 1

Take the Laplace transform of the following initial value
problem and solve for Y(s)=L{y(t)}: y′′−2y′−35y=S(t)y(0)=0,y′(0)=0
where S is a periodic function defined by S(t)={1,0≤t<1 0,
1≤t<2, and S(t+2)=S(t) for all t≥0. Hint: : Use the formula for
the Laplace transform of a periodic function.
Y(s)=

Problem #16:
Use the Laplace transform to solve the following initial value
problem,
y′′ − 5y′ − 36y =
δ(t − 8),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.

Use the Laplace transform to solve the following initial value
problem,
y′′ − 5y′ − 36y =
δ(t − 8),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.

Use the Laplace Transform to solve the following initial value
problem:
11. y′′ −y′ −6y={0 for0<t<2; e^t for t>2}, y(0)=3,
y′(0)=4

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)=?

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