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Differential Equations Cheat Sheet (DRAFT) by

College Diff Eq class

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Defini­tions

Ordinary Differ­ential Equation
Contains deriva­tives of one or more functions with respect to one variable
Classi­fic­ation by Order
Highest order of derivative in equation
Solution of the Equation on Interval I
Any function defined on an interval I and possessing at least n deriva­tives that are continuous on I, which when substi­tuted into an nth order differ­ential reduces the equation to an identity
Classi­fic­ation by linearity
F has to be linear in each of its deriva­tives. The power on each term of y will need to be 1.

Initial Value Problems

Consists of a differ­ential equation and a set of conditions that should be true for a solution and its deriva­tive. The order on the highest derivative is the amount of initial conditions needed to find an exact equation.
 

Examples

Verify that the indicated function is a solution to the differ­ential equation

Linearity

Determine whether the Differ­ential Equation is linear or nonlinear