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Slope Field Generator for First-Order ODEs

Slope Field Generator for First-Order ODEs
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2021-01-01 04:29
FunctionCalculusDerivativeSlider AnimationGraphing
This example demonstrates how to visualize a first-order differential equation y'(x)=f(x,y) using a slope field (direction field), and how to combine it with numerical ODE solving from initial conditions to display solution behavior. The key mathematical ideas are one-variable first-order differential equations, slope fields, initial value problems (IVPs), numerical solutions of ODEs, and the use of numerical integration as part of computing quantities related to the solution. Construction in GeoGebra: the function f is used with the command SlopeField to generate the slopefield grid over user-chosen ranges (xmin/xmax, ymin/ymax) with parameters controlling resolution (e.g., n and delta). The command SolveODE is used alongside multiple numericalIntegral objects (numericalIntegral1 … numericalIntegral8) to perform required numerical calculations. Interactive inputs are handled via Textfield and InputBox objects (InputBox1/2/3, along with parameters A, B, C, D), and visibility controls such as showSF and showA/showB/showC/showD manage what is displayed. Descriptive text objects (text1, text2) annotate the results. Suitable for upper-secondary to early university calculus/DE instruction and for exploratory learning and classroom demonstrations.

GeoGebra Commands & Parameters

  1. Textfield(f) → InputBox1
  2. SlopeField(f, n, L) → slopefield1
  3. SolveODE(f, x(A), y(A), xmax, delta) → numericalIntegral1
  4. SolveODE(f, x(A), y(A), xmin, delta) → numericalIntegral2
  5. SolveODE(f, x(B), y(B), xmax, delta) → numericalIntegral3
  6. SolveODE(f, x(B), y(B), xmin, delta) → numericalIntegral4
  7. SolveODE(f, x(C), y(C), xmax, delta) → numericalIntegral5
  8. SolveODE(f, x(C), y(C), xmin, delta) → numericalIntegral6
  9. SolveODE(f, x(D), y(D), xmax, delta) → numericalIntegral7
  10. SolveODE(f, x(D), y(D), xmin, delta) → numericalIntegral8
  11. Textfield(delta) → InputBox2
  12. Textfield(A) → InputBoxA
  13. Textfield(B) → InputBoxB
  14. Textfield(C) → InputBoxC
  15. Textfield(D) → InputBox3

AI Drawing Prompt Reference

Create a direction-field (slope field) visualization for a first-order differential equation y'(x)=f(x,y). Use an adjustable density setting to generate a slope-field grid over user-chosen x and y ranges, and include a separate editable step-size parameter for numerical computation. Then take four sets of initial conditions entered through text inputs, and for each one numerically integrate the differential equation over the specified x-intervals to capture the resulting solution behavior. Display the slope field together with the numerical solution behavior from the four initial conditions in the same coordinate plane, and add brief text annotations describing what is shown.
The prompt above was compiled from the original drawing commands and is for reference only.