# Thread: Integration for Input x Loss

1. ## 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!

2. ## Re: Integration for Input x Loss

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.