key term - K

Definition

In the equation dy/dx = ky, k represents a constant value that determines how fast y changes with respect to x. It affects both the direction and magnitude of the change in y.

Related terms

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.