How do I find a function from a differential equation? Hey, I'm looking for a guide on how I find Q given the following, where $a$ and $b$ are constants:
\begin{equation}
\frac{dQ}{dt} = \frac{a + Q}{b}
\end{equation}
I have the answer and working for specific case I'm trying to solve but do not understand the steps involved. A guide on how I can solve this, with an explanation of each step would be much appreciated.

Edit: Your particular differential equation can be solved without any calculation if you know the solutions of $$\frac{dQ}{dt} = Q$$, i.e. $C\exp(t), C\in\mathbb{R}$.
Note that, if $f$ is a solution to $\frac{dQ}{dt} = \frac 1b Q$, then $f-a$ is a solution to your equation, therefore is suffices to only look at $a=0$.
The chain rule can be used to see, that if $f$ solves $\frac{dQ}{dt} = Q$, then $f(t/b)$ solves $\frac{dQ}{dt} = \frac 1b Q$.
Therefore all your solutions are of the form $C\exp(t/b) - a, C\in\mathbb{R}$.

Old Post:
I think these differential equations can be solved by "Separation of Variables". See the Wikipedia for a guide. It's got examples! =)
