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Slope Field for y'=-y/x First Order Differential Equation

Slope Field for y'=-y/x First Order Differential Equation
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2026-01-06 22:34
FunctionCoordinate GeometryCalculusDerivativeGraphing
In collections Differential equation Material
This example demonstrates the slope field of the first-order differential equation y'=-y/x, visually showing the distribution and trends of solutions. Core mathematical concepts include differential equations, slope fields, solution curves, and analytical geometry. Key construction elements involve commands like Textfield, SlopeField, SolveODE, and objects such as InputBox1, n, a, slopefield1, text1, etc., for dynamic slope field visualization and solution computation. Suitable for high school students and math enthusiasts studying the geometric meaning and methods of differential equations.

GeoGebra Commands & Parameters

  1. Textfield(f) → InputBox1
  2. SlopeField(f, n, a) → slopefield1
  3. Textfield(a) → InputBox2
  4. Textfield(c) → InputBox3
  5. Textfield(d) → InputBox4
  6. SolveODE(f, c, d, 5, b) → numericalIntegral1
  7. Textfield(b) → InputBox5

AI Drawing Prompt Reference

Create a slope field plot for the first-order differential equation y' = -y/x. Include input panels to specify the function, the grid density n, the sampling range endpoint a, and the initial/parameter values c and d. Use these to generate the slope field on the coordinate plane, showing how the direction (tangent slopes) varies across points and revealing the overall trends of solution curves. Then, using the given c and d together with the parameter 5, compute and display the corresponding numerical integral/solution object as an additional result on the same figure.
The prompt above was compiled from the original drawing commands and is for reference only.