This is documentation for an obsolete product.

# SolveODE

SolveODE[eqns, y, {x, xmin, xmax}] finds a numerical solution to the ordinary differential equations eqns for the function y with the independent variable x in the range xmin to xmax.
SolveODE[eqns, y, {x, xmin, xmax}, {t, tmin, tmax}] finds a numerical solution to the partial differential equations eqns.
SolveODE[eqns, {, , ... }, {x, xmin, xmax}] finds numerical solutions for the functions .

Examples

### Using InstantCalculators

Here are the InstantCalculators for the SolveODE function. Enter the parameters for your calculation and click Calculate to see the result.

### Entering Commands Directly

You can paste a template for this command via the Text Input button on the SolveODE Function Controller.

This command finds a numerical approximation to a function that is equal to its first derivative at each point x between and , and that has the value when x is . SolveODE returns an InterpolatingFunction object.

This can be plotted by making a function from the InterpolatingFunction object.

Here is another example. This finds a numerical approximation to a function whose square is equal to its first derivative.

The warning is appropriate, since this function goes to as it approaches 1 along the horizontal axis.

Here is how to see a graph of an approximation to the function which is the reciprocal of its derivative.
Not too surprisingly, this plot looks very much like the square root function.

Solving systems of equations works similarly. For systems of two equations a so-called phase plot is often a good way to visualize the solution. Here is a phase plot that describes the motion of a weakly damped pendulum.

Clear the function definition.