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

It would be a great opportunity
Answer:
The cost written as a fraction is --> 4 13/99
Step-by-step explanation:
Let x = 4.131313
100x = 413.1313
So, 100x - x = 99x
100(4.131313) - 4.131313 = 408.99, or 409 when rounded
x = 409/99
x = 4 13/99