is: an equation which involves the first derivative and/or higher derivatives of a quantity. [P5.3, P5.4, M6.1]
has as its order: the order of the highest derivative appearing in the equation. [M6.1, P5.3, P5.4]
has as its degree: the highest power of the derivative of highest order appearing in the equation. [M6.1, P5.3, P5.4]
has a general solution: which involves one or more arbitrary constants with values that have to be determined by boundary conditions which are characteristic of the problem being considered. [M6.1, P5.3, P5.4]
See differential equations in the Maths handbook for further details.
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