Applied Mathematics · Ch 5 — Differential Equations and Modeling
Degree of a Differential Equation
Degree of a Differential Equation
The degree of a differential equation is defined only when the equation is a polynomial equation in its derivatives — that is, every derivative appearing in it occurs raised to a positive integral power, with none of the derivatives trapped inside a non-polynomial expression such as a sine, an exponential, or a fractional or negative power.
When this condition holds, the degree is the highest power (a positive integer) to which the highest-order derivative is raised.
Not every differential equation has a defined degree. If the highest-order derivative appears inside a transcendental function or with a non-integral power, the equation simply isn't a polynomial in its derivatives, and its degree is undefined — say so rather than force a number. …