A differential equation is an equation that contains at least one derivative of an unknown function, either an ordinary derivative or a partial derivative. Suppose the rate of change of a function y with respect to x is inversely proportional to y, we express it as dy/dx = k/y.
In calculus, a differential equation is an equation that involves the derivative (derivatives) of the dependent variable with respect to the independent variable (variables). The derivative represents nothing but a rate of change, and the differential equation helps us present a relationship between the changing quantity with respect to the change in another quantity. y=f(x) be a function where y is a dependent variable, f is an unknown function, x is an independent variable. Here are a few differential equations.
- (dy/dx) = sin x
- (d2y/dx2) + k2y = 0
- (d2y/dt2) + (d2x/dt2) = x
- (d3y/dx3) + x(dy/dx) – 4xy = 0
- (rdr/dθ) + cosθ = 5
