Dy/dx = f(x,y)

Definition

This notation represents a general form of a first-order ordinary differential equation, where y is dependent on x and its derivative dy/dx is equal to some function f(x,y). It describes the relationship between the rate of change of y with respect to x.

Related terms

Slope Fields:

Slope fields are graphical representations that help visualize solutions to differential equations like dy/dx = f(x,y). They show how the slope (rate of change) varies across different points on a plane.

Direction Field:

Direction fields also represent solutions to differential equations but focus on indicating the direction in which solutions tend to move at each point rather than their exact slopes.

Differential Equation:

A differential equation relates an unknown function with its derivatives. In this case, dy/dx = f(x,y) represents a specific type called first-order ordinary differential equation, involving only one independent variable (x) and one dependent variable (y).