How to define the derivative of a function

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Hello,

I want to tell Sage what expression to use for the derivative of a funtion a. This vould be something like this: diff(a,t) = b^2. But this doesn't do the trick...

Example I want to define this set of differential quations:

• aDot = da/dt = b^2,
• bdot = db/da = u.

I want Sage to find the relation between a and u. For that Sage needs to differentiate a twice: - diff(a,t,2) But to be able to calculate d^2/d t ^2 a = d/dt *b^2 = 2 bu, Sage needs to to both differential equations.

How can I implemant that?

Thanks alot in advance for your replies!

Johannes