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}
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 | - |