How to Use
Enter the function f (x,y) in the text input field marked "y'=f(x,y)=".

 Example: y'=y

Click the "Graph" button (this button also refreshes the graph).

Choose the initial value point (x0,y0).

 Example: (x0,y0)=(0,1)

This can be done either of two ways:

To erase the graph and all input fields, click the "Clear" button.
 Function of x only: y'=cos(x)

 Exponential Growth: y'=y

 Exponential Decay: y'=-y

 Logistics Growth: y'=y(1-y)

 Semicircles: y'=-x/y

 Radial Lines: y'=y/x

Other Notes
The particular solution function y(x) to the differential equation satisfying the given initial values will be graphed in blue.

The particular solution function y(x) is graphed by determining a numerical approximation to the function using the classical (order four) Runge-Kutta Method (which, in the case where the function f (x,y) is actually a function of the single variable x, reduces to Simpson's Rule for integrating functions of the form f (x) -- see the function of x only example above).

Since this method encounters problems continuing the approximation near points of vertical tangency, the algorithm sets conditions which should stop the approximation prior to reaching such a point -- in the semicircles example above, this has the effect of keeping the graphs of the semicircles from quite reaching the x-axis.