TYPES of DIFFERENTIAL EQUATIONS

DIFFERENTIAL EQUATIONS

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Types Of Differential Equations And Definitions

Home 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 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 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 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 where g(t) and r(t) are arbitary functions of t. For example is a first-order linear differential equation where and Nonlinear Differential Equation It is a differential equation whose right hand side is not a linear function of the dependent variable. For example Homogeneous Differential Equation A linear first-order differential equation is homogeneous if its right hand side is zero , that is For example , 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 . For example is nonhomogeneous.

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