# Integration for Input x Loss

• Jun 16th 2012, 07:48 PM
YujiSato
Integration for Input x Loss
Hello,

I really need help with something I've been working.

I have this model in which I have a stock, an input and a loss rate.
This is the thing:

dN/dt = N * L + A
N is the stock
L is the loss rate for the time period (constant)
A is the input (constant)

So, I wanted to have it integrated, so I would have N as a function of initial N (N0), time, loss and input.
N ~ N0, t, L, A

Can anyone tell me how the function would turn to be?

If someone could also explain how can this integration be done that would be amazing, but solving it would be already of huge help.

Thank you!
• Jun 17th 2012, 01:40 AM
Prove It
Re: Integration for Input x Loss
Quote:

Originally Posted by YujiSato
Hello,

I really need help with something I've been working.

I have this model in which I have a stock, an input and a loss rate.
This is the thing:

dN/dt = N * L + A
N is the stock
L is the loss rate for the time period (constant)
A is the input (constant)

So, I wanted to have it integrated, so I would have N as a function of initial N (N0), time, loss and input.
N ~ N0, t, L, A

Can anyone tell me how the function would turn to be?

If someone could also explain how can this integration be done that would be amazing, but solving it would be already of huge help.

Thank you!

Write it as \displaystyle \begin{align*} \frac{dN}{dt} - L\,N = A \end{align*} and then use an integrating factor.