First-degree differential equation
A first-degree differential equation is a differential equation that is linear in its highest-order derivative. Explicitly, of the independent variable is , the dependent variable is , and the order is it has the form:
Relation with explicit differential equations
First-degree differential equations are typically solved by converting them to explicit differential equations. This simply involves dividing by . The explicit differential equation form is:
However, when doing this division, we may throw away some solutions where . These solutions can be checked for separately, but we can note that these are differential equations of a lower order (specifically, order at most ) hence presumably easier to solve.