ODE(1D) 1st Order Gallery

This is one of the sub-galleries of the ODE Gallery. See the ODE documentation for general information about ODEs and ODE galleries in 3D-XplorMath-J.

The exhibits in the "ODE(1D) 1st Order" Gallery are first-order ordinary differential equations in one dimension. The equation that defines such an ODE has the form

x'(t) = f(t,x)

where x(t) is a real-valued function. A solution x(t) has its values in the real numbers and could be visualized as a point that moves along a line as t changes. However, in 3D-XplorMath-J, the solution is visualized by displaying the graph of the solution function y = x(t). That is, the point (t,x(t)) in the plane is plotted for each value of t. Note that in this gallery, the value of the solution function x(t) at time t is represented by the vertical axis, while the horizontal axis represents time. A direction field is also shown by default as part of the visualization. This field represents the slope of the tangent line to the solution curve at each point. (The direction field can be hidden using a command in the "Action" menu.)

To specify an initial condition for the ODE, initial values must be provided for t and x. You can input an initial point using the input boxes in the Control Panel. Alternatively, you can use the mouse to select an initial point by clicking with the middle mouse button, or by using the left mouse button while holding down the ALT key (the Option key on Mac's).