Question

Use the Laplace transform to solve the given initial-value problem. y'' + y = f(t), y(0) = 0, y'(0) = 1, where f(t) = 0, 0 ≤ t < π 5, π ≤ t < 2π 0, t ≥ 2π

Answer #1

Use the Laplace transform to solve the given initial-value
problem.
y'' + 6y' +
34y = δ(t −
π) + δ(t −
7π), y(0) =
1, y'(0) = 0

Use the Laplace transform to solve the given initial-value
problem.
y'' + 10y' +
41y = δ(t −
π) + δ(t −
7π), y(0) =
1, 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

Use the Laplace transform to solve the given initial-value
problem. y'' − 7y' + 12y = (t − 1), y(0) = 0, y'(0) = 1

Use the Laplace transform to solve the given initial-value
problem.
y'' − 6y' + 13y = 0, y(0) = 0, y'(0) =
−5
#14 7.3
y(t) ?
please show work and circle the answer

Use the laplace transform to solve for the initial
value problem:
y''+6y'+25y=delta(t-7)
y(0)=0 y'(0)=0

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 to solve initial value
problem
y"+4y'+20y=delta(t-2)
y(0)=0, y'(0)=0
use step t-c for uc(t)

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 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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