Assume that I have a nonlinear, non-trivial under-determined system of the sort
$$4a+b^2+\sin(c)=5 \tag 1$$ $$b-c^2+d=3 \tag 2$$
It is my goal to find the rules between the parameters by which we can obtain solutions to the under-determined system of equations. A simple way would, of course, be to simply re-order the equations above, so that we have for each parameter something like:
$$a = 5-b^2-\sin(c)$$
Unfortunately, this only seems to work for the parameters $a$ and $d$ - for the parameters $b$ and $c$ we have more than one option to express it in terms of other variables. Hence my questions:
- Is there a recommended, structured way of finding these equivalence relations even when they occur in multiple equations?
- Is there a way of creating a node tree of sorts to see how the other parameters change if we fix one of the previously free parameters?
(The real system I am interested in is a LOT more complicated, and I want to see what happens if I fix different free parameters.)