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Classification of Differential Equations Partial Differential Equations. Linear Differential Equations. Non-linear Differential Equations. Homogeneous Differential Equations.

We can place all differential equation into two types: ordinary differential equation and partial differential equations. A partial differential equation is a differential equation that involves partial derivatives. An ordinary differential equation is a differential equation that does not involve partial derivatives.

Partial differential equations occur in many different areas of physics, chemistry and engineering. Second order P.D.E. are usually divided into three types: elliptical, hyperbolic, and parabolic.

The different types of differential equations are: Ordinary Differential Equations. Homogeneous Differential Equations. Non-homogeneous Differential Equations. Linear Differential Equations. Nonlinear Differential Equations.

The order of a differential equation is defined to be that of the highest order derivative it contains. The degree of a differential equation is defined as the power to which the highest order derivative is raised. The equation (f?)2 + (f?)4 + f = x is an example of a second-degree, third-order differential equation.

Systems of equations can be classified by the number of solutions. If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent .

We will classify these equations into three different categories. If b2 ? 4ac > 0, we say the equation is hyperbolic. If b2 ? 4ac = 0, we say the equation is parabolic. If b2 ? 4ac < 0, we say the equation is elliptic.

A first order homogeneous linear differential equation is one of the form y2032+p(t)y=0 y 2032 + p ( t ) y = 0 or equivalently y2032=2212p(t)y.

Introduction to Differential Equations Ordinary differential equations or (ODE) are equations where the derivatives are taken with respect to only one variable. That is, there is only one independent variable. Partial differential equations or (PDE) are equations that depend on partial derivatives of several variables.

There are two major classes of ODE's, linear and nonlinear.