Question

Use the definition of the Laplace transform to solve the IVP:

4y''− 4y' + 5y = δ(t), y(0) = −1, y'(0) = 0.

Answer #1

y'' + 4y' + 5y = δ(t − 2π),
y(0) = 0, y'(0) = 0
Solve the given IVP using the Laplace Transform. any help
greatly appreciated :)

Use the Laplace transform to solve the following, given the
initial conditions: y^'' +5y^'+4y = 0 y(0)=1,y^' (0)=0.

Use the Laplace transform to solve the following IVP
y′′ +2y′ +2y=δ(t−5) ,y(0)=1,y′(0)=2,
where δ(t) is the Dirac delta function.

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)=?

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 IVP:
y′(t) +y(t) = cos(t),
y(0) = 0.

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′′−4y′−32y=δ(t−6)y(0)=0,y′(0)=0

Use Laplace Transforms to solve the following IVPs .
4y′′+4y′+5y=−t ; y(0)=0 , y′(0)=0

Use
Laplace transform to solve IVP
2y”+2y’+y=2t , y(0)=1 , y’(0)=-1

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