Substitution into differential equations in Maxima

Question

let's say I have several differential equations in the following form

where the variables in the pointed brackets are complex numbers for example

My question is whether it is possible in the Maxima to write down at first the set of the differential equations in the form mentioned above without evaluation the derivatives, then make the substitutions for the variables in the pointed brackets and after that evaluate the derivatives and separate the real and imaginary parts.

Maxima allows functions and values to be undefined in expressions, so you can write things like `diff(foo(t),t) = bar(t) + baz*quux` and functions `foo` and `bar` and values `baz` and `quux` can all be undefined. So without knowing more about it, it seems like what you want to do should be possible just as you described it. Maybe you can give more details. — Robert Dodier, Jul 26 '21 at 19:18

slitvinov · Accepted Answer · 2021-08-08T14:02:32.550

You can consider this example (it illustrates what Robert Dodier wrote in comments).

(%i1) depends(x, t) $
(%i2) e: diff('bra(x), t) + diff('bra(x), t);
                                   d
(%o2)                           2 (-- (bra(x)))
                                   dt
(%i4) e, bra, diff;
                           d               d
(%o4)                   2 (-- (re(x)) + j (-- (im(x))))
                           dt              dt

Substitution into differential equations in Maxima

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