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Exact Differential Equation

Exact Differential Equation
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2019-08-25 21:35
CalculusDerivativeIntegral
In collections First Order DE Solving Techniques
This example demonstrates the solution process of an exact differential equation. Key mathematical concepts include integration and derivatives in calculus. Using GeoGebra commands such as RandomElement, Simplify, and Integral, the solution process is dynamically illustrated. Suitable for university calculus courses.

GeoGebra Commands & Parameters

  1. RandomElement(aLst) → a
  2. RandomElement(bLst) → b
  3. RandomElement(cLst) → c
  4. Simplify(RandomElement[MLst]) → M
  5. IndexOf(M, MLst) → ind
  6. Simplify(Element[NLst, ind]) → N
  7. Simplify(N(x, y) - Integral[Derivative[N(x, y), x], x]) → NN
  8. Integral(M(x, y), x) → ans1
  9. Integral(NN(x, y), y) → ans2
  10. Simplify(ans1(x, y) + ans2(x, y)) → Ans

AI Drawing Prompt Reference

Illustrate the solution process of an exact differential equation, dynamically showing the application of integration and derivatives in calculus. Randomly select three functions, compute the derivative of one, then integrate and simplify to obtain the solution of the equation, and finally draw the solution expression.
The prompt above was compiled from the original drawing commands and is for reference only.