Exploring an ODE

This applet displays the direction field and solutions for an ordinary differential equation (ODE).

Enter an ODE in the textbox for $\frac{dy}{dx}$.
The ODE’s direction field is shown in green. Click ‘Show direction field’ to show/hide it.

Click ‘Show solution’ to display the solution of the ODE subject to a given initial condition. You can set the initial condition by typing in the boxes or by dragging the blue point. What is the relationship between the direction field and the solution curve?

Other resources:

Geogebratube page for this applet

Related applet with Euler method