Question

y'' + 4y' + 5y = δ(t − 2π),

y(0) = 0, y'(0) = 0

Solve the given IVP using the Laplace Transform. any help greatly appreciated :)

Answer #1

Use the definition of the Laplace transform to solve the
IVP:
4y''− 4y' + 5y = δ(t), y(0) = −1, y'(0) = 0.

Use the Laplace transform to solve the following initial value
problem:
y′′−4y′−32y=δ(t−6)y(0)=0,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 Laplace Transforms to solve the following IVPs .
4y′′+4y′+5y=−t ; y(0)=0 , y′(0)=0

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 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)=?

solve the IVP
y'' - 4y' - 5y = 6e-x, y(0)= 1, y'(0) =
-2

Use the Laplace transform to solve the IVP:
y′(t) +y(t) = cos(t),
y(0) = 0.

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

solve the following DE using laplace transform
y"+4y'+4y=0; y(0)=-2, y'(0)=9

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