What is a differential equation

Answer 1

A differential equation is an equation involving derivatives.

A derivative is the rate of change of a dependent variable with respect to one or more independent variables.

Below are two different examples of differential equations;

Example 1

d²x/dt² + a(dx/dt) + kx = 0

where t is the independent variable and x is the dependent variable, while a and k are coefficients.

Example 2

∂u/∂x - ∂u/∂y = x - 2y

where x and y and independent variables and u is the dependent variable.

Note that Example 1 is an ordinary differential equation and Example 2 is a partial differential equation.