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Linear Differential Equation Solver - Slope Field & General Solution

Linear Differential Equation Solver - Slope Field & General Solution
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2016-11-23 11:50
FunctionCalculusDerivativeIntegralGraphing
This GeoGebra applet visualizes the solution process for first-order linear differential equations. It demonstrates core calculus concepts including slope fields, general solutions, and integration constants. Construction utilizes SolveODE for symbolic solving, SlopeField for direction visualization, and InputBox/Textfield for interactive parameter control and step-by-step explanation. Ideal for high school or university students studying differential equations to understand solution behavior and geometric interpretation.

GeoGebra Commands & Parameters

  1. Integral(P, x) → J
  2. Simplify((-J(x))) → K
  3. Simplify(ℯ^(J(x))) → I
  4. Integral((I(x) * Q(x))) → f
  5. Simplify(f) → g
  6. Textfield(P) → InputBox1
  7. Textfield(Q) → InputBox2
  8. SlopeField(H(x, y)) → slopefield1
  9. SolveODE(H(x, y)) → h
  10. LaTeX((I(x) * Q(x))) → modText

AI Drawing Prompt Reference

Create a visual for a first-order linear differential equation solver. Show a slope field with direction arrows representing slopes at grid points, and overlay several solution curves from the general solution family. Include two input boxes for the coefficient function and the right-hand side function, and display the integrating factor expression nearby. The scene should emphasize the geometric relationship between the slope field and the solution curves, suitable for calculus education.
The prompt above was compiled from the original drawing commands and is for reference only.