Differential Equation:
Any equation that can be taken the derivative of. An equation is the ANSWER.
Ex.

General Solution:
The differential equation Integrated (Has +C in solution)
Ex.

The Initial Condition:
A point on the curve that helps us solve for the Particular Solution.
Ex.

Particular Solution:
The general solution, that has the Initial Condition in, and +C has been solved for.
Ex.

Long Example:

Directly Proportional Differential Equations:

Example of Directly Proportional Differential Equations:

Family of Solutions:
When there are multiple functions in a slope field, because of different C values.

Line Elements:
What the slope of the tangent is at every point.
AKA
They are parallel with the function.