Consider the initial value problem y″+16y=48t, y(0)=3,y′(0)=7. take the laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. denote the laplace transform of y(t) by y(s). do not move any terms from one side of the equation to the other (until you get to part (b) below).

Step-by-step explanation:

We are given that initial value problem

y(0)=3,y'(0)=7

Using the formula then,

Substitute the values then, we get

Taking Laplace inverse on both sides then we get

y(t)=

Using formula:

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: