Introduction to Ordinary Differential Equations I

A comprehensive set of vocabulary flashcards covering key concepts in Ordinary Differential Equations.

Differential Equation

A mathematical relation involving derivatives of unknown functions with respect to independent variables.

Order of a Differential Equation

The highest derivative present in the equation.

Degree of a Differential Equation

The power of the highest order derivative after removing radicals and fractions.

Ordinary Differential Equation (ODE)

An equation that relates functions of a single independent variable and their derivatives.

Partial Differential Equation (PDE)

An equation that relates functions of two or more independent variables and their derivatives.

Classification by Type

Differential equations can be classified as ordinary or partial based on the number of independent variables.

Homogeneous Differential Equation

An equation where all terms depend on the function and its derivatives, equated to zero.

Non-homogeneous Differential Equation

An equation that includes a term that is a function of only the independent variable.

Linear Differential Equation

A differential equation where the unknown function and its derivatives appear linearly.

Nonlinear Differential Equation

A differential equation where the unknown function and/or its derivatives are of degree greater than one.

General Solution

A solution to a differential equation that contains arbitrary constants.

Particular Solution

A specific solution obtained by assigning values to the arbitrary constants.

Singular Solution

A solution that cannot be formed by assigning specific values to the arbitrary constants in the general solution.

Method of Eliminating Arbitrary Constants

A technique for formulating differential equations by differentiating a general solution to remove constants.

Variable Separable Equation

A first-order differential equation where variables can be separated into functions of x and y.

System of Differential Equations

A set of equations involving multiple dependent variables and their derivatives.

First Order and First Degree Differential Equation

A differential equation whose highest derivative is of the first order and has the highest power of one.

Analytical Solution

An explicit formula for the solution that involves elementary functions.

Numerical Solution

An approximate solution obtained using computational algorithms for complex differential equations.

Explicit Solution

A solution of the form y=f(x), expressing y solely in terms of x.

Implicit Solution

A solution expressed as F(x, y) = C, defining a relationship between x and y.