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I wonder what is the best way to solve this equation in MA?

$$ y= \frac{\partial}{\partial x} ~ \frac{\partial}{\partial x^*} f $$

where y and x are functions of time, so that this should be written as

$$ y(t) = \frac{\partial}{\partial t} / \frac{\partial x}{\partial t} \big( \frac{\dot{f}}{\dot{x^*}} \big) $$

Any help how to write this consistently in MA and solve to get f(t) ? I don’t know I think it can be solved as an integration problem by NIntegrate or by DSolve at arbitrary initial conditions.

Edit:

Here is what I have tried

eqf = D[(f'[t]/x*'[t]), t]/x'[t]

Is this syntax right?

Then I used DSolve wich give me undesired result at all, because it's in terms of an integration

DSolve[y[t] == eqf, f[t], t]

So any idea to do this in smarter way ?

Thanks!

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  • 1
    $\begingroup$ What do you know about f? $\endgroup$ – Ulrich Neumann Oct 11 at 7:40
  • $\begingroup$ Are x[t], y[t]] known functions? $\endgroup$ – Alex Trounev Oct 13 at 14:35

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