MHB How Do You Rearrange dS/dt = (n-x-rS)(L-1) to Solve for t?

[BSLAHi]

Hello,

I have been given a general equation that is dS/dt = (n-x-rS)(L-1)
and it needs to be rearranged in order to for the subject to be t.

I have spent a while trying to find a way to attempt this but with no luck
so I will leave this here.

Thanking You,
BSLAHi

 

[Olinguito]

Hello BSLAHi.

You can separate the variables and integrate.
$$\frac{\mathrm dS}{\mathrm dt}\ =\ (n-x-rS)(L-1)$$
$\displaystyle\implies\ \int\frac{\mathrm dS}{n-x-rS}\ =\ \int(L-1)\,\mathrm dt$.