Classifying second-order Partial differential equations

What does it mean when it says to classify the second-order partial differential? (See attached)
How would I get started?
 

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Linear second order PDE's can, by a change of coordinates, be written in one of three (technically four, but one is degenerate) standard forms, called elliptic, parabolic, and hyperbolic equations. Any introductory PDE textbook should contain a description of these three types of equations. See e.g. http://www.math.psu.edu/tseng/class/Math251/Notes-PDE pt1.pdf
 

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Partial differential equations with constant coefficients can be so classified. If there are variable coefficients, the equation may change from "parabolic" to "hyperbolic" to "elliptic" depending on the value of the independent variables.
 
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Partial differential equations with constant coefficients can be so classified. If there are variable coefficients, the equation may change from "parabolic" to "hyperbolic" to "elliptic" depending on he value of the independent variables.
Good catch. Thanks.
 

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