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Question: How to define an operator?

Question:How to define an operator?

444083220 10 Maple
February 23 2020
1

Could anyone help me with the following task?

The simplest case is, for example, 

    If y=y(x). Denote y'(x)=Dx(y). Then we make a change of veriables :

    x=φ(z,w), y=ψ(z,w), where z independent and w=w(z),

    Now the ODE: y'(x)=1 turns to:

    Dz(y)/Dz(x)=1,  i.e. ψz+w'(z)ψw=φz+w'(z)φw.

    So we have the relation: Dz=(φz+w'(z)φw)Dx.

    The task is how to define the operators (Dx, Dz) to transform more complecated ODE of (x,y) (e.g. (Dx+F(x,y))5(y)=0,   

     F arbitrary) to its counterpart of (z,w)?

Thank you in advance!
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