First-Order Differential Equation
The first-order differential equation is defined by an equation: dy/dx = f(x, y). It involves two variables x and y, where the function f(x, y) is defined on a region in the xy-plane. For any linear expression in y, the first-order differential equation [Tex]y’ = f (x, y)[/Tex] is linear. Nonlinear differential equations are those that aren’t linear.
First Order Differential Equation
A first-order differential equation is a type of differential equation that involves derivatives of the first degree (first derivatives) of a function. It does not involve higher derivatives. It can generally be expressed in the form: dy/dx = f(x, y). Here, y is a function of x, and f(x, y) is a function that involves x and y.
It defined by an equation dy/dx = f (x, y) where x and y are two variables and f(x, y) are two functions. It is defined as a region in the xy plane. These types of equations have only the first derivative dy/dx so that the equation is of the first order and no higher-order derivatives exist.
Differential equations of first order is written as;
y’ = f (x, y)
(d/dx)y = f (x, y)
Let’s learn more about First-order Differential Equations, types, and examples of First-order Differential equations in detail below.