TYPES OF DIFFERENTIAL EQUATIONS (ACCORDING TO INDEPENDENT VARIABLES)

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There are two types of differential equations according to the numbers of independent variables.

For example, we have a differential equation:

(dy)/(dx) = cos(x)

(dy)/(dx) = cos(x) the variable y in this equation is called the dependent variable.

(dy)/(dx) = cos(x) the variable x in this equation is called the independent variable.


Now, since we defined what a dependent and independent variables are we can now determine the types of differential equations according to the numbers of independent variables:

1. Ordinary Differential Equations – it is a differential equation that contains only one independent variable.

For example (Independent variables are in bold characters):

L{ [(d^2)(y)] / (dt)^2 } + R [ (di)/(dt) ] + (1/C)i = ewcos(wt)

[ (d^3)(y)/(dx)^3 ]^2 – x [ (d^2)(y)/(dx)^2 ]^3 + x^3 = 0


2. Partial Differential Equations – it is a differential equation that contains two or more independent variables.

For example (Independent variables are in bold characters):

[ (∂x)/(∂y) ] + 2y[ (∂x)/(∂z) ] = 3

[ (∂^2)(u)/(∂x)^2 ] + [ (∂^2)(u)/(∂y)^2 ] + [ (∂^2)(u)/(∂z)^2] = 0

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