Equation order and degree
Equation order and degree [ edit ] The order of the differential equation is the order of the highest derivative of the unknown function that appears in it. When a differential equation is written as a polynomial equation in the unknown function and its derivatives, its degree is, depending on the context, the degree in the highest derivative of the unknown function, [12] or its total degree in the unknown function and its derivatives. In particular, a linear differential equation has degree one for both meanings, but the non-linear differential equation � ′ + � 2 = 0 is of degree one for the first meaning but not for the second one. An equation containing only first derivatives is a first-order differential equation , an equation containing the second derivative is a second-order differential equation , and so on. [13] [14] Differential equations that describe natural phenomena ...