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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Differential Equations (Notes, Lecture, and Examinations)
Non-FictionThis book contains the compilation of our notes, lecture notes and articles about Differential Equations. We are publishing this book to share our understanding about the subject matter. Please, kindly leave a vote if you find this book helpful. Tha...
