# How to Understand Differential Equations

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Differential equations contain at least one derivative function of one or more variables. They are useful for describing changing quantities and their rates of change in a variety of disciplines ranging from economic to physics. Differential equations are usually not taught until at least the junior level in college and a student will need a background in integral calculus.

• Begin your study with first order ordinary differential equations (ODEs.) This form contains a function of one dependent variable and the first derivative with respect to one independent variable. This is the simplest possible true differential equation and must be thoroughly understood before advancing.

• Take up second order ODEs. These equations involve first and second derivatives. They also have linear and non-linear forms, but only linear homogenous equations where the differential equation is equal to zero should be studied at this point.

• Examine non-homogeneous ODEs. These differential equations are equal to a function of the independent variable. It should be understood that only special cases of these types of equations can be solved.

• Advance to partial differential equations (PDEs.) These equations involve a function of multiple independent variables and its partial derivatives with respect to those variables. PDEs must be covered thoroughly as they have practical applications in many disciplines, particularly engineering.

• Study additional topics throughout the course. Fourier series, LaPlace transforms and systems of differential equations may be taught at different points in the course.

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