Question

Solve the initial value problem using Laplace transforms. Explain and show all steps.

y'' + 9y = 3δ(t - π)

where y(0) = 3 and y'(0) = 0

Answer #1

Use Laplace Transforms to solve the initial value problem for
y(t). Show all steps. Circle your answer.
y''+ 6y' + 9y = 90t^(4)e^(−3t)
y(0)= -2 , y'(0)= 6

Solve the initial value problem using Laplace transforms y "+
2ty'-4y = 1; y (0) = y '(0) = 0.

Solve the initial value problem below using the method of
Laplace transforms. y''-y'-30y=0, y(0) = 4 , y'(0) = 46
y(t) = ?

1. Solve the following initial value problem using Laplace
transforms.
d^2y/dt^2+ y = g(t) with y(0)=0 and dy/dt(0) = 1 where g(t) = t/2
for 0<t<6 and g(t) = 3 for t>6

Use the method of Laplace transforms to solve the following
initial value problem. y'' + 6y' + 5y = 12e^t ; y(0) = −1, y'(0) =
7

Solve the initial value problem below using the method of
Laplace transforms.
ty'' - 4ty' + 4y = 8, y(0) = 2, y'(0) = -5

Use the method of laplace transforms to solve the following
Initial Value Problem:
y"+2y'+y=g(t), y'(0)=0

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

Solve the initial value problem. Explain and show all steps.
y'' - 4y' +4y = 0
where y(0) = 1 and y'(0) = 2

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.

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