The following applet can be used to draw "slope fields" for the differential equation y' = f(x,y). Simply enter the function f(x,y) and the values a and b. The applet automatically draws a sample solution through the point (a,b). The values a and b can be changed by simply typing a new value, such as "1.2345", "pi/2", "sqrt(5)+cos(3)", etc. You may also change these values by using the up/down arrow keys or dragging the corresponding point left or right. To move the center of the graph, simply drag any point to a new location. To label the x-axis in radians (i.e. multiples of pi), click on the graph and press "control-r". To switch back, simply press "control-r" again.

\displaystyle \frac{dy}{dx} = x \cos y

## Software/Applets used on this page

This page uses an applet from David Little (Lecturer in the Mathematics Department, Penn State University, USA) and is used with his permission.

## Glossary

### differential equation

An equation containing an independent variable, dependent variable and derivatives of the dependent variable with respect to the independent variable.

### equation

A statement that two mathematical expressions are equal.

### function

A rule that connects one value in one set with one and only one value in another set.

### graph

A diagram showing a relationship between two variables.

The diagram shows a vertical y axis and a horizontal x axis.

The diagram shows a vertical y axis and a horizontal x axis.

### sample

A collection of sampling units drawn from a sampling frame.

### solution

the answer to a problem.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|

AP Calculus AB (USA) | 4 | 1st Order Differential Equations | Slope fields | - |

AP Calculus BC (USA) | 4 | 1st Order Differential Equations | Slope fields | - |

AQA A-Level (UK - Pre-2017) | FP3 | 1st Order Differential Equations | Slope fields | - |

AQA A2 Further Maths 2017 | Pure Maths | Solving Differential Equations | Slope Fields - Extra | - |

AQA AS/A2 Further Maths 2017 | Pure Maths | Solving Differential Equations | Slope Fields - Extra | - |

CCEA A-Level (NI) | FP2 | 1st Order Differential Equations | Slope fields | - |

Edexcel A-Level (UK - Pre-2017) | FP2 | 1st Order Differential Equations | Slope fields | - |

Edexcel A2 Further Maths 2017 | Core Pure Maths | Differential Equation Methods | (1st) Slope Fields | - |

Edexcel AS/A2 Further Maths 2017 | Core Pure Maths | Differential Equation Methods | (1st) Slope Fields | - |

I.B. Higher Level | 9 | 1st Order Differential Equations | Slope fields | - |

Methods (UK) | M11 | 1st Order Differential Equations | Slope fields | - |

OCR A-Level (UK - Pre-2017) | C4 | 1st Order Differential Equations | Slope fields | - |

OCR A2 Further Maths 2017 | Pure Core | Solving Differential Equations | Slope Fields - Extra | - |

OCR MEI A2 Further Maths 2017 | Core Pure B | Solving Differential Equations | Slope Fields - Extra | - |

OCR-MEI A-Level (UK - Pre-2017) | DE | 1st Order Differential Equations | Slope fields | - |

Universal (all site questions) | F | 1st Order Differential Equations | Slope fields | - |

WJEC A-Level (Wales) | C4 | 1st Order Differential Equations | Slope fields | - |