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Exact Differential Equation Solver

Exact Differential Equation Solver
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2019-09-02 02:20
CalculusDerivativeIntegral
In collections First Order DE Solving Techniques
This example demonstrates how to solve exact differential equations using GeoGebra. Key mathematical concepts include methods for solving differential equations. The commands used in the construction include text field, derivative, integral, simplify, slope field, and more. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Textfield(M) → InputBox1
  2. Textfield(N) → InputBox2
  3. Derivative(M, y) → M_y
  4. Derivative(N, x) → N_x
  5. Integral(M, x) → intM
  6. Simplify(N(x, y) - Integral[Derivative[N, x], x]) → NN
  7. Integral(NN, y) → intNN
  8. Simplify(intM(x, y) + intNN(x, y)) → intsum
  9. SlopeField(f, 40, 0.5, -8, -8, 8, 8) → SlopeF
  10. ImplicitCurve(intsum) → eq1

AI Drawing Prompt Reference

Draw the solution of an exact differential equation. First, input functions M and N, then calculate the derivative of M with respect to y and the derivative of N with respect to x. Compute the indefinite integral of M and the indefinite integral of N with respect to x, simplify N minus the integral of M with respect to x, and then compute the indefinite integral of the simplified expression with respect to y. Finally, add the two integrals together to get the final solution, and plot the slope field and implicit curve.
The prompt above was compiled from the original drawing commands and is for reference only.