How to define the derivative of a function
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!