High permormance symbolic computing

[landau_rules]

Dear all,

I have derived a set of differential equations. One is still missing and its left hand side is called f (as in the attachment). Unfortunately f is known only implicitly.

I am not very familiar with maple or mathematica. My question is:

Is it possible to obtain the expression for f with maple or mathematica? Can the problem be tackled with the mathematica commands "integrate" or "dsolve"?

What about symbolic computations in general. Are there free powerfull codes out there, which have certain advantages over the commercial products maple or mathematica, so that i can run them on a workstation?

Best greetings from Europe
K.

 

[jvicens]

Dear K.,

Thank you for reaching out with your question. It is certainly possible to obtain the expression for f using both Maple and Mathematica. Both software have powerful symbolic computation capabilities that can handle differential equations and implicit functions.

In Maple, you can use the "dsolve" command to solve the differential equation and obtain an explicit expression for f. For example, if your differential equation is represented as "f'(x) = x^2 + f(x)", you can use the command "dsolve(f'(x) = x^2 + f(x), f(x))" to obtain the solution for f.

In Mathematica, you can use the "DSolve" command in a similar manner to obtain the explicit expression for f. Both Maple and Mathematica also have the option to solve differential equations numerically if an explicit solution is not possible.

As for free powerful codes, there are several options available such as SageMath, Maxima, and SymPy. These codes have the advantage of being open-source and can be run on a workstation without any additional cost. However, they may not have the same level of user-friendly interface as Maple or Mathematica. It ultimately depends on your specific needs and preferences.

I hope this helps and best of luck with your research.