# Question:How do I substitute higher derivatives for variables?

## Question:How do I substitute higher derivatives for variables?

Maple

I am using Maple to generate PDEs. I have expressions of the form p(dx,dy,dz, etc.) where p is a nonlinear polynomial. I would like to substitute d/dx for dx etc and then later apply the resulting differential equation to a function. I am having multiple problems with this.

1. Maple seems to be unable to handle a derivative unless there is a function for the derivative to act on. (This is not a huge issue, but it would be helpful.)

2. Even if I do specify a function Maple maps dx^3 to diff(f,x)^3 not diff(f,x,x,x). I was able to use the subs command to get around this for one variable, however dx^2*dy was mapped to diff(f,x,x)*diff(f,y).

Replacing derivatives by hand is not an option as the polynomials are of large degree and in several variables. What would be the most efficient way to rewrite my equation as a PDE?

Any suggestions would be welcome.

Thank you very much.

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