MA 266 Exam 1

General Solution

Function with an arbitrary constant, such as y = C

Particular Solution

No arbitrary constant, such as y = 1

Mathematical Model

Newton’s law of heating/cooling

Population model

Initial Value Problem

An IVP is a differential equation together with some given initial condition(s)

Solution to a differential equation is usually a general solution

Solution to an IVP is usually a particular solution

Existence and Uniqueness Theorem

Equilibrium solution

constant y solution (like y = 1) satisfying a differential equation. Horizontal line on a slope field.

For velocity questions, it is referred to as the limiting velocity (the velocity when t = ∞)

Finding equilibrium solutions

Set y’ = 0

Solving first order linear differential equations

Definition of Homogeneous DE

Bernoulli DE Shortcut

Exact DE

signs matter

Test whether DE is exact