To solve such an equation, we first ``separate the variables'' as shown.

We now integrate both sides to obtain the solution

We then proceed to find the particular solution, as before.

As an example, we will use the equation, arising in physics, modelling
radioactive decay. Here, is a constant known in physics
as the ``decay constant''. represents the number of undecayed
nuclei, and is the time in seconds. The equation is

(The negative sign shows that is decreasing.) To solve the equation, we separate the variables to obtain

We now integrate both sides to find the general solution.

Here, represents the initial number of undecayed nuclei - the number at .