Does someone have a solution for the following equation where the carrying capacity varies linearly with time (and only time):
$\frac{\mathrm dN}{\mathrm dt}= rN\left(1-\frac{N}{K}\right)$
$K = m \cdot t + b$ where $m$ and $b$ are constant.
I'm looking for a solution that models population growth with a linearly increasing upper limit:
I'm looking for an equation that is in the form of $N$ as a function of $t$ where $r$, $m$, and $b$ are constants.
Sorry, the last math class I took was multivariate calculus in college, so I'm not even sure this is a valid question.