Discover published sets by community

The highest derivative in a differential equation.

A differential equation that is not linear, meaning it may involve powers or products of the dependent variable and its derivatives that are higher than the first degree.

A differential equation of the form $M(x, y)dx + N(x, y)dy = 0$, for which there exists a function $F(x, y)$ such that $dF = Mdx + Ndy$, implying $\frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}$.

A differential equation where every term is a function of the dependent variable and its derivatives; in other words, there are no terms that are functions of the independent variable alone.

A differential equation in which the variables can be separated on opposite sides of the equation, allowing the equation to be written in the form $g(y)\,dy = f(x)\,dx$.

A differential equation that has terms that are functions of the independent variable alone or involve no derivatives of the dependent variable.

A differential equation accompanied by a specification of the value of the dependent variable and/or its derivatives at a particular point.

A type of differential equation where the solution must satisfy certain fixed conditions, called boundary conditions, at the end-points of the interval where the solution is defined.

A differential equation in which the dependent variable and its derivatives appear to the first power, and the equation does not contain products of the dependent variable and its derivatives.