>> 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.
>>

Solve solves this:

>>> solve(log(f(t).diff(t))-log(t), f(t).diff(t))
[t]

/c

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