P-derivation, also known as partial derivation, typically refers to the process of finding the derivative of a function with respect to one of its variables while keeping the other variables constant. This concept is commonly used in multivariable calculus, where functions depend on multiple variables. For a function \( f(x, y, z, \ldots) \), the partial derivative with respect to \( x \) is denoted as \( \frac{\partial f}{\partial x} \).
An algebraic differential equation is a type of differential equation that involves algebraic expressions in the unknown function and its derivatives, but does not involve any transcendental functions like exponentials, logarithms, or trigonometric functions. Essentially, it is a differential equation where the relationship between the function and its derivatives can be expressed entirely in terms of polynomials or rational functions.