Slope Fields and Solving Differential Equations

Slope Fields - A graphical representation of a differential equation. They are used to visualize the parallel curves that constitute a family of general solutions to a differential equation without actually solving it.

Examples:

dy/dx = x-y/2



Differential Equations
A differential equation contains one or more terms involving derivatives of one variable with respect to another variable.


Example:



This is a general solution to a differential equation.
Another thing you can do is find the particular solution if you are given an initial condition.

Example:

y(2)=-1



-1=1/3(2)^3 + C
C = -11/3
y = 1/3x^2 -11/3