DIFFERENTIAL EQUATIONS

Types Of Differential Equations And Definitions

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DE Definition Types of DE

Odinary Differential Equations

An Ordinary Differential Equation is a differential equation that depends on only one independent varialble.

For example
Example of an ODE is an Odinary Differential Equation because y(the independent variable) depends only on t(the independent variable)

Partial Differential Equations

A Partial Differential Equation is differential equation in which the dependent varialble depends on two or more independent variables.

For example
The Laplace's equation The Laplace's equation is a Partial Differential Equation because f depends on two independent variables x and y.

Order of a Differential Equation

The order of a differential is the order of the highest derivative entering the equation. 

For example
The equation A second order DE is called a second-order differential equation because it involves second derivatives.

Linear Differential Equation

A first-order differential equation is linear if it can be written in the form A linear DE where g(t) and r(t) are arbitary functions of t.

For example
An example of a linear DE is a first-order linear differential equation where g(t) = t^2 and r(t) = cos(t)

Nonlinear Differential Equation

It is a differential equation whose right hand side is not a linear function of the dependent variable.

For example
A non linear DE

Homogeneous Differential Equation

A linear first-order differential equation is homogeneous if its right hand side is zero , that is r(t) = 0

A Homogeneous DE

For example
An example of homogeneous DE , where k is a constant, is homogeneous.

Nonhomogeneous Differential Equation

A linear first-order differential equation is nonhomogeneous if its right-hand side is non-zero that is r(t) is not equal to zero.

A nonhomogeneous DE

For example
An example of a nonhomogeneous DE is nonhomogeneous.


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