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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} = x+xy+y

Software/Applets used on this page

David Little
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

the answer to a problem.

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-