I am trying to formulate a mathematical model as part of an op-research problem, and I'm running into a roadblock concerning differential equations of a certain kind; I was hoping to understand if there are any mathematical techniques to handle them.
To give you the problem statement, I have a certain mathematical equation of the following form :
$$f (x) = a \cdot x – b \cdot ( f '(x) )^2 + c \cdot f ''(x)$$
Here $f '$ and $f ''$ and first order and second order derivatives.
I'd like to know if there is an analytical way to measure the sensitivity of function $f$ with respect to the parameters $a$, $b$ and $c$. I know there are ways to handle this numerically, but I'm looking for an analytical method. It would be great if you have any pointers to do this, or any references I can check out, or a ready solution.