Mercyhurst UniversityMath DeptDr Williams Home

Slope Fields

dy/dx =

x Interval: [ , ]
y Interval: [ , ]

Enter expression using the variables x and y. Use only () for grouping symbols.

Available Operations:
+   -   *   /   ^   %   !

Available Functions:
sqrt() abs() ceil() floor() log() log2() log10()
sin() cos() tan() csc() sec() cot()
asin() acos() atan() acsc() asec() acot()

e   i   LN2   LN10   pi   SQRT2   SQRT1_2

Display Options
Click and drag the graph to change the view.


Segment Spacing:

Scale length by magnitude of rate of change
Color segment by magnitude of rate of change

Euler's Method:
Sketch y with initial condition y'() =
Follow mouse on hover

Save as PNG

Slope Fields

Slope fields can be used to visualize the solutions of a first order differential equation of the form \[ \frac{dy}{dx} = f(x,y) \] where \(y\) is a function of \(x\). At any point \((x,y)\) in the Cartesian plane, the value of \(\frac{dy}{dx} = f(x,y)\) gives us the slope of the tangent line to the graph of the differential equation's solution. By drawing short line segments with that slope at several points, we can begin to see the "shape" of the solutions of the differential equation.

About the Applet

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This applet was last updated February 2020.