Dear Sage users,
Is it possible in Sage to define a function with the help of its
derivative?
Example:
Given the system of linear differential equations
dy1(t)/dt = a(t)y1(t) + b(t)y2(t)
dy2(t)/dt = c(t)y1(t) + d(t)y2(t),
where a, b, c, d are known functions of t.
In Maple y1(t) and y2(t) can be defined as
> define(y1, diff(y1(t), t) = a(t) * y1(t) + b(t) * y2(t))
> define(y2, diff(y2(t), t) = c(t) * y1(t) + d(t) * y2(t))
In Maple it is possible to manipulate with y1(t) and y2(t) without
solving the system of equations.
Does there exist a Sage-construct equivalent to the Maple-construct
given above?
Regards,
Pieter
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