Get C Code of InverseFunction and Eliptical Integral of First Kind?

Questions
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1

Hello;

I have the below output for a nonlinear differential equation.
I want to c-code the answer (in PIC-C). But I dont understand what the answer is mathematically. Can you help?

Here is the code:

DSolve[{-x^2 + (0.231486 - 0.2290576*cos[y[x]]) Derivative[1][y][
      x]^2 == 0, y[0] == Q1, y'[0] == 0}, y[x], x]

result.JPG
result.JPG626Ă—218 23.7 KB

2

Try

sol = NDSolve[{-x^2 + (0.231486 - 0.2290576*Cos[y[x]]) Derivative[1][y][x]^2 == 0, y'[0] == 0}, y, {x, 0, 2}]

sol.png
sol.png881Ă—577 18.2 KB

3

Hello Shengui;

Thanks for this suggestion. In the output it gives me an interpolating function but i dont see what the function is?
What are the coefficients and degree etc?
Interpolating functions seem embedded inside mathematica so its not possible to see what the function is. Therefore i cannot code it in c environment.
Anyother suggestions?

4

Hello Shengui;

Thanks for this suggestion. In the output it gives me an interpolating function but i dont see what the function is?
What are the coefficients and degree etc?
Interpolating functions seem embedded inside mathematica so its not possible to see what the function is. Therefore i cannot code it in c environment.
Anyother suggestions?

5

You will be better off solving this ODE numerically in C. I believe InverseFunction will also use numerical methods to compute results.

6

Can you give me an example? Which numerical method would be the best alternative for coding in C?

7

Numerical ODE solving is a whole topic on its own. It is covered in many books. Take a look e.g. at Numerical Recipes, which has a very gentle introduction, if I recall correctly.

8

If you want something quick and clear, I highly recommend you to checkout Dr. Shen’s videos on

Pick the control points from Mathematica’s InterpolationFunction (assign x to some values and evaluate them) and use the formulae presented in the videos above.