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While differential equations have three basic types?ordinary (ODEs), partial (PDEs), or differential-algebraic (DAEs), they can be further described by attributes such as order, linearity, and degree.

Linear equations must involve y,y?,y? etc. with coefficients that are (at worst) functions of x. ... If the ODE has the unknown function and/or its derivative(s) as an argument of a trigonometric, hyperbolic trigonometric, exponential, logarithmic, and/or n-th root function, the ODE is non-linear.

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.

Types of Differential Equations Ordinary Differential Equations. Partial Differential Equations. Linear Differential Equations. Nonlinear differential equations. Homogeneous Differential Equations. Nonhomogeneous Differential Equations.

First-order PDEs are usually classified as linear, quasi-linear, or nonlinear. The first two types are discussed in this tutorial. A PDE which is neither linear nor quasi-linear is said to be nonlinear.

Homogeneity of a Linear DE. where Fi(x) F i ( x ) and G(x) are functions of x, the differential equation is said to be homogeneous if G(x)=0 G ( x ) = 0 and non-homogeneous otherwise.

If differential equations can be written as the linear combinations of the derivatives of y, then they are called linear ordinary differential equations. These can be further classified into two types: Homogeneous linear differential equations. Non-homogeneous linear differential equations.