A first order differential equation can be written as $ \frac{dy}{dx}=f(x,y) $ where f is some function that depends on x and y.
One simple example is the equation $ \frac{dy}{dx}=-ay+b $. If a is not 0, and y is not b/a, then we can rewrite this as follows: $ \frac{dy/dx}{y-(b/a)}=-a $
Integrating this gives $ ln|y-(b/a)|=-ax+C $ so the general solution is then $ y=(b/a)+ce^{-ax} $
