Question

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

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 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 for the initial
value problem:
y''+6y'+25y=delta(t-7)
y(0)=0 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'' + 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 = f(t), y(0) = 0, y'(0) = 1, where f(t) = 0, 0 ≤ t
< π 5, π ≤ t < 2π 0, t ≥ 2π

Use the Laplace transform to solve the given initial-value
problem. Use the table of Laplace transforms in Appendix III as
needed.
y'' + 25y = cos 5t, y(0) =
3, y'(0) = 4

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) =...

Given the second order initial value problem
y′′+y′−6y=5δ(t−2), y(0)=−5, y′(0)=5
Y(s) denote the Laplace transform of y. Then
Y(s)=
Taking the inverse Laplace transform we obtain
y(t)=
y(t)=

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