First Order Differential Equation FAQs

First Order Differential Equation Questions

What is First Order Differential Equation?

A first order differential equation is a differential equation where the maximum order of a derivative is one and no other higher-order derivative can appear in this equation. A first-order differential equation is generally of the form [Tex]dy/dx =f (x,y)[/Tex].

What are the types of First Order Differential Equations?

First Order Differential Equations are classified into three categories: (i) Separable Differential Equation, (ii) Linear Differential Equation and (iii) Exact Differential Equation

Give one example of First Order Differential Equation.

An Example of First Order Differential Equations: (dy/dx = 2x)

What are application of First Order Differential Equations?

First Order Differential Equation are used in various fields like physics, engineering, biology, applied mathematics, etc.

What is Homogeneous First Order Differential Equation?

A first order differential equation M(x, y) dx + N(x, y) dy = 0 is said to be homogeneous if both M(x, y) and N(x, y) are homogeneous. We can write a homogeneous linear first-order differential equation is of the form y’ + p(x)y = 0.

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.