$ x,y,z$ are known functions of $t$ and $f$ is a known function:
$$ z(t)= f ( x(t),y(t)) ; $$
In order to compute $t$ as a function of $x$(or other dependent variables) how to define some differential equation as $$ \frac{dt}{dx}= F (x,y,z,t)$$
or in any other suitable differential equation form to find $t$ as a dependent variable ?