Question

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. |

Answer #1

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′′ − 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 ′+ 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) =...

Solve for Y(s), the Laplace transform of the solution y(t) to
the initial value problem below. y''-9y'+18y=5te^(3t), y(0)=2,
y'(0)=-4

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 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

Consider the following initial value problem.
y′ + 5y =
{
0
t ≤ 2
10
2 ≤ t < 7
0
7 ≤ t < ∞
y(0) = 5
(a)
Find the Laplace transform of the right hand side of the above
differential equation.
(b)
Let y(t) denote the solution to the above
differential equation, and let Y((s) denote the
Laplace transform of y(t). Find
Y(s).
(c)
By taking the inverse Laplace transform of your answer to (b),
the...

How to use laplace transform to solve the following
problem ?
y'' - 10y' +9y = 5t , given y(0)=-1, y'(0)=2

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