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Differential Equations

Euler's Formula
Differential Equations

Types of Differential Equations

Aside from identities, theorems, and tautologies, a differential equation is an equation that includes a differential. This is a very broad scope which includes many equations which are used explicitly or unconsciously in many kinds of everyday calculations as well as the daunting and formidable equations of highly technical subjects.

Differential Equations can be roughly divided into three broad types which are further defined by attributes which may cut across the categories.

Ordinary Differential Equations (ODE are differential equations which involve differentials of only one dependent variable and express a relationship to one independent variable.

Partial Differential Equations involve partial differentials of one dependent variable in relation to two or more independent variables.

Total Differential Equations involve differentials of two or more dependent variables in relation to one independent variable.

Diffential equations are further distinguishable by several other attribute.

The order of a differential equation is the highest order differential that occurs in the equation.


Sources:

Ince, Edward L. [1926], Ordinary Differential Equations

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