It looks like the ODE is

with the initial condition of
.
Rewrite the right side in terms of the unit step function,

In this case, we have

The Laplace transform of the step function is easy to compute:

So, taking the Laplace transform of both sides of the ODE, we get

Solve for
:

We can split the first term into partial fractions:

If
, then
.
If
, then
.


Take the inverse transform of both sides, recalling that

where
is the Laplace transform of the function
. We have


We then end up with

Answer:
Option 2) When the x-value is 0, the y-value is 1.
Step-by-step explanation:
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
or
In a proportional relationship the constant of proportionality k is equal to the slope m of the line <em>and the line passes through the origin
</em>
Remember that in a direct variation
For x=0, the value of y is equal to zero too
therefore
The graph is not a direct variation , because
When the x-value is 0, the y-value is 1.
Y = -5x -5
To check, we can insert 0 for y and -1 for x
0 ? (-5X-1) - 5
0 ? 5 - 5
0 = 0
So yes, the equation is correct
Answer:
18
hope this helps
have a good day :)
Step-by-step explanation: