A direction field (or slope field / vector field) is a picture of the general solution to a first order differential equation with the form [math]\frac{dy}{dx} = f(x,y)[/math]

[list][br][*]Edit the gradient function [math]f^{\prime}(x,y)[/math] in the input box at the top. The function you input will be shown in blue underneath as [math]dy/dx=f(x,y)[/math][br][*]The Density slider controls the number of vector lines.[br][*]The Length slider controls the length of the vector lines.[br][*]Adjust [math]x_{min}, x_{max}, y_{min}[/math] and [math]y_{max}[/math] to define the limits of the slope field.[br][*]Check the Solution boxes to draw curves representing numerical solutions to the differential equation.[br][*]Click and drag the points A, B, C and D to see how the solution changes across the field.[br][*]Change the Step size to improve or reduce the accuracy of solutions (0.1 is usually fine but 0.01 is better). [br]If anything messes up....hit the reset button to restore things to default.[br][/list]