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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} = \sqrt{x^2+y^2}

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.

### sample

A collection of sampling units drawn from a sampling frame.

### solution

Full Glossary List

## This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AP Calculus AB (USA)41st Order Differential EquationsSlope fields-
AP Calculus BC (USA)41st Order Differential EquationsSlope fields-
AQA A-Level (UK - Pre-2017)FP31st Order Differential EquationsSlope fields-
AQA A2 Further Maths 2017Pure MathsSolving Differential EquationsSlope Fields - Extra-
AQA AS/A2 Further Maths 2017Pure MathsSolving Differential EquationsSlope Fields - Extra-
CCEA A-Level (NI)FP21st Order Differential EquationsSlope fields-
Edexcel A-Level (UK - Pre-2017)FP21st Order Differential EquationsSlope fields-
Edexcel A2 Further Maths 2017Core Pure MathsDifferential Equation Methods(1st) Slope Fields-
Edexcel AS/A2 Further Maths 2017Core Pure MathsDifferential Equation Methods(1st) Slope Fields-
I.B. Higher Level91st Order Differential EquationsSlope fields-
Methods (UK)M111st Order Differential EquationsSlope fields-
OCR A-Level (UK - Pre-2017)C41st Order Differential EquationsSlope fields-
OCR A2 Further Maths 2017Pure CoreSolving Differential EquationsSlope Fields - Extra-
OCR MEI A2 Further Maths 2017Core Pure BSolving Differential EquationsSlope Fields - Extra-
OCR-MEI A-Level (UK - Pre-2017)DE1st Order Differential EquationsSlope fields-
Universal (all site questions)F1st Order Differential EquationsSlope fields-
WJEC A-Level (Wales)C41st Order Differential EquationsSlope fields-