Exponential Growth/Decay: When k is positive, it leads to exponential growth where y increases rapidly over time. When k is negative, it results in exponential decay where y decreases rapidly over time.
Equilibrium Solution: For certain values of k, there may exist an equilibrium solution where dy/dx = 0. This means that y remains constant and does not change with respect to x.
Initial Condition:To find a specific solution to the differential equation dy/dx = ky, an initial condition is required. This condition provides the value of y at a particular x-value.