Ordinary Differential Equation Vocabulary

A set of vocabulary flashcards covering Ordinary Differential Equations topics including exact equations, higher degree ODEs, higher order homogenous equations, variable coefficients, and variation of parameters.

Ordinary Differential Equation (10 Hours)

A syllabus topic allocated 10 Hours covering first order first degree, first order higher degree odes, and higher order linear differential equations.

Exact differential equation

A type of first order first degree differential equation studied alongside integrating factors in ordinary differential equations.

Integrating factors

Factors used in the resolution of non-exact first order first degree differential equations to make them exact.

First order higher degree odes

Ordinary differential equations of the first order with a degree greater than one, categorized by being solvable for $p$, $y$, and $x$.

Solvable for p, y and x

Solution techniques applied to first order higher degree odes by expressing the equation in terms of $p$, $y$, or $x$.

Homogenous equations higher order

Higher order differential equations whose solutions involve finding complementary functions and particular integrals.

Complementary functions

Functions representing the general solution to the homogeneous linear differential equation of higher order.

Particular Integrals

Integrals that form part of the complete solution for non-homogeneous linear differential equations alongside complementary functions.

Linear differential equation with variable coefficient

A differential equation in which coefficients are not constant, including Cauchy's Euler and Legendre's equations.

Cauchy's Euler equation

A specific form of linear differential equation with variable coefficient studied in ordinary differential equations.

Legendre's equation

A type of linear differential equation with variable coefficient addressed alongside Cauchy's Euler equation.

Method of variation of parameters

A general method used for finding solutions or particular integrals of differential equations.