Having a dependent variable (say V(x,t)) which has dependency on independent variables, say k(x,t), r(x), l(x), t(x), how can we find a PDE in terms of x and t?
We can find PDE for new polynomials by using
series method Or by finding the rising operators J+ and lowering operators J- for the required polynomials f(x,y)_{n} , for more details see for example
Associated Laguerre–Konhauser polynomials,
quasi-monomiality and operational identities
Maged G. Bin-Saad
https://core.ac.uk/download/pdf/82444478.pdf
please read this research :
http://repository.sustech.edu/bitstream/handle/123456789/15597/%E2%80%AB%D9%85%D8%A8%D8%A7%D8%AF%D9%8A%D8%A1%20%D8%A7%D9%84%D9%85%D8%B9%D8%A7%D8%AF%D9%84%D8%A7%D8%AA%20%D8%A7%D9%84%D8%AA%D9%81%D8%A7%D8%B6%D9%84%D9%8A%D8%A9%E2%80%AC%20.pdf?sequence=1&isAllowed=y
Usually by taking derivatives, of the functions, and finding a relations between these derivatives, results in a differential.
Dear Garima Dahiya
Usually, one needs to solve a given partial differential equation.
You asked for an inverse problem.
I think you have some functions related to each other by some modeling process, and you need to express the relations using PDE.
Your request is not possible without clarifying what the relations are!
More explanation for your question is needed to reply to your request.
Best regards
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