Question

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

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 following initial value
problem:
y′′−4y′−32y=δ(t−6)y(0)=0,y′(0)=0

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'' + 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.
y'' − 6y' + 13y = 0, y(0) = 0, y'(0) =
−5
#14 7.3
y(t) ?
please show work and circle the answer

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′′ − 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.

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 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

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