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symbolic-mathmaxima

Substitution into differential equations in Maxima

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

enter image description here

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

enter image description here

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.

Solution

  • 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