What is the best computational software(free/cheap)? I have already tried Wolfram Alpha (not pro) and I don't know whether I can access MATLAB for free, any software than downloaded for free and is easy to use will work. I need it for computing complex Hermite polynomials and solving differential equations of order more than 3.
 A: Regarding MatLab. If you're a student or staff member at an institute (or work at a company) that has taken a MatLab license, you can also use it using your official mail ID. They also give licenses to participants in some competitions. You could consider exploring these avenues first, since MatLab is the state of the art in scientific computation.
If you are still unable to obtain/ afford a license for whatever reasons, consider these alternatives:

*

*SciLab: Download link.


*GNU Octave: Dpwnload link.
These two are by far the best alternatives. They are both Open Source and from reliable developers, and offer similar functionality to MatLab. At the very least, you can be reasonably sure that they will be maintained in the foreseeable future.
Another option that might work well for you is FreeMat, which is a MatLab clone.
Depending on your use cases, SciPy/ NumPy, or R might also be good options.
Otherwise, you can also consider options like Modelica.
As you can see, there is hardly a dearth of great options for you to choose from :)

Edit:
Seeing that you intend to work with Hermite polynomials and differential equations, Python and R can definitely work. In fact, you can probably work with any programming language, even without libraries, but you wanted a software or similar, and these should work.
A: I suggest looking at Octave, a free Matlab-like replacement.
Also consider SageMath.
https://www.sagemath.org/
A: Here are some free alternatives to matlab, although from my experience none are going to really be quite up to par.
