Explicit differential equation
An explicit differential equation is a differential equation where the highest-order derivative is explicitly written as a function of the independent variable, dependent variable, and lower order derivatives. Explicitly, if the independent variable is , the dependent variable is , and the order is , it has the form:
where is a function of variables.
Relation with first-degree differential equations
Any explicit differential equation is a first-degree differential equation. Conversely, any first-degree differential equation can be converted to an explicit differential equation via division by a function, though we may need to add back certain solutions that are identically zeros for the function.