# Integral curves

An integral curve is a parametric curve that represents a specific solution to an ordinary differential equation (ODE) or system of equations $\left(\begin{array}{c}\stackrel{˙}{x}\left(t\right)\\ \stackrel{˙}{y}\left(t\right)\end{array}\right)=F\left(x,y\right)$.

## Syntax

```integral_curves(List)
```
```integral_curves(List, Identifier)
```
```integral_curves(List, Identifier, Range)
```
```integral_curves(List, Identifier, Range, Identifier, Range)
```

## Description

Given a list with the function $F$ (a two-elements list), returns a sample of solutions of the ODE.

Given a list with the function $F$ (a two-element list) and an identifier: the first variable (the $x$ in the notation used above) returns a sample of solutions of the ODE.

Given a list with the function $F$ (a two-elements list) and an identifier: the first variable (the $x$ in the notation used above) returns a sample of solutions of the ODE in the given range for the variable $x$.

Given a list with the function $F$ (a two-elements list) and two identifiers: the variables $x$ and $y$ , following the notation above, returns a sample of solutions of the ODE in the given ranges.

## Options

Below is a complete list of options that may be used in the `integral_curves` function.

Option

Description

Format

Default value

number_of_solutions

Number of solutions to be plotted

Natural. `{number_of_solutions = 25}`

10