I have one more question about this part:
> 1. Convert the system to a matrix.

Do some other parts of sympy do this in a way that can catch nonlinear
equations that can trivially be transformed into linear ones. For
instance log(f'(t))=log(t) -> f'(t)=t.

Obviously sometimes the transformations are valid only over a certain
domain and probably there are other issues but maybe `solve()` already
does some of this magic.

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