Solve the differential equation dy/dt = ky, where k is a constant.
To solve the differential equation dy/dt = ky, we can use separation of variables. 

First, rewrite the equation as:

dy/y = k dt

Now integrate both sides with respect to their respective variables:

∫(1/y) dy = ∫k dt

The left side integrates to ln|y| (plus a constant), and the right side integrates to kt (plus another constant):

ln|y| = kt + C₁

Now exponentiate both sides to get rid of the natural logarithm:

|y| = e^(kt + C₁)

We can rewrite e^(C₁) as another constant, say C₂:

|y| = C₂e^(kt)

Since |y| is always positive, we can drop the absolute value signs:

y(t) = C₂e^(kt)

This is the general solution to the given differential equation, where C₂ is an arbitrary constant determined by initial conditions.