Order of Partial Differential Equation

What is a Partial Differential Equation?

Partial Differential Equation is also called PDE. It is a differential equation containing partial derivatives of the dependent variable with one independent variable. For any function f(x1, x2,…,xn) its partial differential equation(PDE) is,...

Order of Partial Differential Equation

Order of the highest derivative term that occurs in a given partial differential equation is called the order of the said equation....

Degree of Partial Differential Equation

Degree of a partial differential equation is the degree of the highest derivative in the PDE. The partial differential equation ∂z/∂x + ∂y/∂x = x + zy has 1 as the highest derivative of the first degree....

General Form of Partial Differential Equation

The general form of Partial Differential Equation is,...

Representing Partial Differential Equation

Partial Differential Equations are represented using subscript and ∂ or ∇ symbol. suppose we have a function f then Partial Differential Equations are given as:...

Types of Partial Differential Equations

Various types of Differential Equations are,...

Classification of Partial Differential Equation

There is a linear second-order partial differential equation of second degree given as Auxx + 2Buxy + Cuyy + constant = 0. Its discriminant is B2 – AC. On the basis of different values of such discriminant, the partial differential equations can be classified as follows,...

Applications of Partial Differential Equations

PDEs are applied in a lot of fields like mathematics, engineering, physics, finance, etc. Some of their applications are as follows:...

How to Solve Partial Differential Equations

There are various methods to solve Partial Differential Equation, such as variable substitution and change of variables, can be used to identify the general, specific, or singular solution of a partial differential equation. Say we have an equation: z = yf(x) + xg(y)....

Steps for Solving Partial Differential Equations

Step I: Differentiate both LHS and RHS w.r.t.x....

Partial Differential Equation Class 12

In many educational systems, including those following the Class 12 curriculum, partial differential equations (PDEs) are often introduced as part of advanced mathematics or physics courses. Class 12 courses typically provide an introductory understanding of partial differential equations, focusing on foundational concepts and solution techniques rather than in-depth mathematical theory or advanced applications....

Partial Differential Equations Examples

Example 1: Given the function c = f(x2 – y2), find its partial differential equation....

Practice Questions on Partial Differential Equations

Q1. Solve PDE ux + 2uy – 4 = 0...

FAQs on Partial Differential Equations

What are Partial Differential Equations?...